%!PS-Adobe-2.1 %%Creator: DECwrite V1.1 %%+Copyright (c) 1990 DIGITAL EQUIPMENT CORPORATION. %%+All Rights Reserved. %%DocumentFonts: (atend) %%EndComments %%BeginProcSet DEC_WRITE 1.06 % Date: Tue, 17 Dec 91 14:49:50 PST % Subject: PS preprint of JPEG article submitted to IEEE Trans on Consum. Elect % From: Greg Wallace % Mods by Tom Lane 18-Dec-91 to avoid use of nonstandard fonts: % Replaced Souvenir-Demi with Helvetica-Bold % Replaced Souvenir-Light with Helvetica % Deleted gratuitous use of AvantGarde for spacing /DEC_WRITE_dict 150 dict def DEC_WRITE_dict begin/$D save def/$I 0 def/$S 0 def/$C matrix def/$R matrix def/$L matrix def/$E matrix def/pat1{/px exch def/pa 8 array def 0 1 7{/py exch def/pw 4 string def 0 1 3{pw exch px py 1 getinterval putinterval}for pa py pw put}for}def/pat2{/pi exch def/cflag exch def save cflag 1 eq{eoclip}{clip}ifelse newpath{clippath pathbbox}stopped not{/ph exch def/pw exch def/py exch def/px exch def/px px 3072 div floor 3072 mul def/py py 3072 div floor 3072 mul def px py translate/pw pw px sub 3072 div floor 1 add cvi def/ph ph py sub 3072 div floor 1 add cvi def pw 3072 mul ph 3072 mul scale/pw pw 32 mul def/ph ph 32 mul def/px 0 def/py 0 def pw ph pi[pw 0 0 ph 0 0]{pa py get/px px 32 add def px pw ge{/px 0 def/py py 1 add 8 mod def}if}pi type/booleantype eq{imagemask}{image}ifelse}if restore}def/PS{/_op exch def/_np 8 string def 0 1 7{/_ii exch def/num _op _ii get def _np 7 _ii sub num -4 bitshift PX num 15 and 4 bitshift -4 bitshift PX 4 bitshift or put}for _np}def/PX{[15 7 11 3 13 5 9 1 14 6 10 2 12 4 8 0]exch get}def/FR{0.7200 0 $E defaultmatrix dtransform/yres exch def/xres exch def xres dup mul yres dup mul add sqrt}def/SU{/_sf exch def/_sa exch def/_cs exch def/_mm $C currentmatrix def/rm _sa $R rotate def/sm _cs dup $L scale def sm rm _mm _mm concatmatrix _mm concatmatrix pop 1 0 _mm dtransform/y1 exch def/x1 exch def/_vl x1 dup mul y1 dup mul add sqrt def/_fq FR _vl div def/_na y1 x1 atan def _mm 2 get _mm 1 get mul _mm 0 get _mm 3 get mul sub 0 gt{{neg}/_sf load concatprocs/_sf exch def}if _fq _na/_sf load setscreen}def/BO{/_yb exch def/_xb exch def/_bv _bs _yb _bw mul _xb 8 idiv add get def/_mk 1 7 _xb 8 mod sub bitshift def _bv _mk and 0 ne $I 1 eq xor}def/BF{DEC_WRITE_dict begin/_yy exch def/_xx exch def/_xi _xx 1 add 2 div _bp mul cvi def/_yi _yy 1 add 2 div _bp mul cvi def _xi _yi BO{/_nb _nb 1 add def 1}{/_fb _fb 1 add def 0}ifelse end}def/setpattern{/_cz exch def/_bw exch def/_bp exch def/_bs exch PS def/_nb 0 def/_fb 0 def _cz 0/BF load SU{}settransfer _fb _fb _nb add div setgray/$S 1 def}def/invertpattern{$S 0 eq{{1 exch sub}currenttransfer concatprocs settransfer}if}def/invertscreen{/$I 1 def/$S 0 def}def/revertscreen{/$I 0 def}def/setrect{/$h exch def/$w exch def/$y exch def/$x exch def newpath $x $y moveto $w $x add $y lineto $w $x add $h $y add lineto $x $h $y add lineto closepath}def/concatprocs{/_p2 exch cvlit def/_p1 exch cvlit def/_pn _p1 length _p2 length add array def _pn 0 _p1 putinterval _pn _p1 length _p2 putinterval _pn cvx}def/OF/findfont load def/findfont{dup DEC_WRITE_dict exch known{DEC_WRITE_dict exch get}if DEC_WRITE_dict/OF get exec}def mark/ISOLatin1Encoding 8#000 1 8#001{StandardEncoding exch get}for /emdash/endash 8#004 1 8#025{StandardEncoding exch get}for /quotedblleft/quotedblright 8#030 1 8#054{StandardEncoding exch get}for /minus 8#056 1 8#217 {StandardEncoding exch get}for/dotlessi 8#301 1 8#317{StandardEncoding exch get}for/space/exclamdown/cent/sterling/currency/yen/brokenbar/section /dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered /macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph /periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter /onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde /Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave /Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde /Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn /germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla /egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis /eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave /uacute/ucircumflex/udieresis/yacute/thorn/ydieresis 256 array astore def cleartomark /encodefont{findfont dup maxlength dict begin{1 index/FID ne{def}{pop pop}ifelse}forall/Encoding exch def dup/FontName exch def currentdict definefont end}def/loads{/$/ISOLatin1Encoding load def/&/encodefont load def/*/invertpattern load def/+/revertscreen load def/-/invertscreen load def/:/concatprocs load def/^/setpattern load def/~/pat1 load def/_/pat2 load def/@/setrect load def/A/arcn load def/B/ashow load def/C/curveto load def/D/def load def/E/eofill load def/F/findfont load def/G/setgray load def/H/closepath load def/I/clip load def/K/kshow load def/L/lineto load def/M/moveto load def/N/newpath load def/O/rotate load def/P/pop load def/R/grestore load def/S/gsave load def/T/translate load def/U/sub load def/V/div load def/W/widthshow load def/X/exch load def/Y/awidthshow load def/a/save load def/c/setlinecap load def/d/setdash load def/e/restore load def/f/setfont load def/g/initclip load def/h/show load def/i/setmiterlimit load def/j/setlinejoin load def/k/stroke load def/l/rlineto load def/m/rmoveto load def/n/currentfont load def/o/scalefont load def/p/currentpoint load def/r/currenttransfer load def/s/scale load def/t/setmatrix load def/u/settransfer load def/w/setlinewidth load def/x/matrix load def/y/currentmatrix load def}def end %%EndProcSet %%EndProlog %%BeginSetup %%BeginFont: Dutch801-Roman-DECmath_Extension % Bitstream Fontware PSO Font -- Version 1.6 % DECmath Font Version 1.0, 4-13-89 % % Copyright 1989 by Bitstream, Inc. All Rights Reserved. % Copyright 1989 Digital Equipment Corporation % % This product is the sole property of Bitstream Inc. and % contains its proprietary and confidential information % U.S Government Restricted Rights % This software product is provided with RESTRICTED RIGHTS. Use, % duplication or disclosure by the Government is subject to % restrictions as set forth in FAR 52.227-19(c)(2) (June, 1987) % when applicable or the applicable provisions of DOD FAR supplement % 252.227-7013 subdivision (b)(3)(ii) (May,1981) or subdivision % (c)(1)(ii) (May, 1987). Contractor/manufacturer is Bitstream Inc. % /215 First Street/Cambridge, MA 02142. % % This software is furnished under a license and may be used and copied % only in accordance with the terms of such license and with the % inclusion of the above copyright notices. This software or any other % copies thereof may not be provided or otherwise made available to any % other person. No title to and ownership of the software is hereby % transfered. % % The information in this software is subject to change without notice % and should not be construed as a commitment by Digital Equipment % Corporation. % % BITSTREAM, INC. AND DIGITAL EQUIPMENT CORPORATION DISCLAIM ALL % WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED % WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL % BITSTREAM, INC. AND DIGITAL EQUIPMENT CORPORATION BE LIABLE FOR ANY % SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER % RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF % CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN % CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. % /n_chars 128 def /DC { /bits exch def /name exch def /num exch def num 256 lt {Encoding num name put} if CharStrings name bits put } bind def /bsd 15 dict def bsd begin /FontType 3 def /FontName /Dutch801-Roman-DECmath_Extension def /PaintType 0 def /UniqueID 440185 def /FontMatrix [.001 0 0 .001 0 0] def /FontInfo 12 dict def /CharStrings 1 n_chars add dict def CharStrings /.notdef <0F> put /Encoding 256 array def 0 1 255 {Encoding exch /.notdef put} for /temp 15 dict def temp begin /get-word { 0 s i get add 8 bitshift /i i 1 add def s i get add 32768 sub /i i 1 add def } bind def /get-byte { s i get 128 sub /i i 1 add def } bind def /get-name { /len s i get def /i i 1 add def s i len getinterval /i i len add def } bind def /eval-arr 16 array def eval-arr 16#00 {get-word 0} bind put eval-arr 16#01 {4 {get-word} repeat setcachedevice newpath} bind put eval-arr 16#02 {closepath 2 {get-word} repeat moveto} bind put eval-arr 16#03 {2 {get-word} repeat lineto} bind put eval-arr 16#04 {6 {get-word} repeat curveto} bind put eval-arr 16#05 {4 {get-word} repeat get-name do-char} bind put eval-arr 16#06 {0 get-word rlineto} bind put eval-arr 16#07 {get-word 0 rlineto} bind put eval-arr 16#08 {0 get-byte rlineto} bind put eval-arr 16#09 {get-byte 0 rlineto} bind put eval-arr 16#0A {2 {get-byte} repeat rlineto} bind put eval-arr 16#0B {6 {get-byte} repeat rcurveto} bind put eval-arr 16#0F {end PaintType 2 eq {temp begin stroke exit} {temp begin fill exit} ifelse } bind put /do-char-arr 16 array def do-char-arr 16#00 {get-word pop} bind put do-char-arr 16#01 {4 {get-word pop} repeat} bind put do-char-arr 16#02 {closepath 2 {get-word} repeat moveto} bind put do-char-arr 16#03 {2 {get-word} repeat lineto} bind put do-char-arr 16#04 {6 {get-word} repeat curveto} bind put do-char-arr 16#05 {4 {get-word} repeat get-name do-char} bind put do-char-arr 16#06 {0 get-word rlineto} bind put do-char-arr 16#07 {get-word 0 rlineto} bind put do-char-arr 16#08 {0 get-byte rlineto} bind put do-char-arr 16#09 {get-byte 0 rlineto} bind put do-char-arr 16#0A {2 {get-byte} repeat rlineto} bind put do-char-arr 16#0B {6 {get-byte} repeat rcurveto} bind put do-char-arr 16#0F {closepath exit} bind put /eval { /s exch def /i 0 def { /t s i get def /i i 1 add def eval-arr t get exec } loop } bind def /do-char { t s i matrix currentmatrix 2 {6 index} repeat translate 2 {8 index 256 div} repeat scale end CharStrings 5 index get temp begin /s exch def /i 0 def { /t s i get def /i i 1 add def do-char-arr t get exec } loop setmatrix [/i /s /t] {exch def} forall 5 {pop} repeat } bind def end /BuildChar { exch begin 0.2 setflat Encoding exch get CharStrings exch 2 copy known not { pop /space } if get temp begin eval end end } bind def FontInfo /version (Fontware-PSO 1.6) put FontInfo /OutlineResolution 1000 put FontInfo /Copyright (Copyright 1989 by Bitstream,Inc. and Digital Equipment Corp. All Rights Reserved.) put FontInfo /Notice (Dutch 801 is a registered trademark of Bitstream, Inc.) put FontInfo /Date (1989/4/13 12:28:18) put FontInfo /FullName (Dutch 801 Roman DECmath_Extension (TM)) put FontInfo /FamilyName (Dutch 801) put FontInfo /Weight (Medium) put FontInfo /ItalicAngle 0.00 put FontInfo /isFixedPitch false put FontInfo /UnderlinePosition -100 put FontInfo /UnderlineThickness 60 put 32 /parenlfs4 <0083180180e27480830280290282cd802a04822b7f7981b47ebd81667dd604 81097cc380e37b7780e37a560480e37934810977e8816676d50481b875e48226753882cd 748109b5048270752e821775c381cd769f04816677cf813f7915813f7a5604813f7b968166 7cdc81cd7e0d0482147ee182747f828302802a094b0F> DC 33 /parenrts4 <008318018015748082348029028015802a0480a37f8381047edf814b7e0d04 81b27cdc81d87b9681d87a560481d8791581b277cf814b769f04810075c280a8752f8015 748109b60480f27539815f75e381b176d504820e77e78235793582357a560482357b76820e 7cc481b17dd60481617ec280ef7f76804b802a094a0F> DC 34 /bracketlfs4 <008247018115748082398029028116802a06745707812308c0077f1e068b2907 80e208c0077edd0F> DC 35 /bracketrts4 <00824701800d74808131802902800e802a08400780e30674d7077f1d084007 8124068ba9077edc0F> DC 36 /bracketlfbts4 <00827f018115748082718033028116803306744e07815b08c0077ee6068b7209 3f0F> DC 37 /bracketrtbts4 <00827f01800d748081698033028128803306748e077ee6084007815b068bb209 3f0F> DC 38 /bracketlftps4 <00827f018115747782718029028116802a06744d09c1068b7307811a08c007 7ea50F> DC 39 /bracketrttps4 <00827f01800d74778169802902800e802a084007811a06748d09c1068bb307 7ea50F> DC 40 /bracelfs4 <0083410180b0748082bd8029028289802a0481df7fdf81857f5681857e9906 7d4d0481857b9981787b4a81547b0604812d7abd80f57a8f80b07a66085f04814779eb8185 7974818578c5067d4a04818575a481a7753e81ee74ed04821c74b9824b749c8289748109b4 08a004821b74e981e6756881e6761206828e0481e6797e81a379e180ef7a560481a57acc 81e67b2a81e67c0b06828e0481e67f41821d7fc382bd800908a1094c0F> DC 41 /bracerts4 <008341018083748082918029028084802a085f0481257fc3815b7f42815b7e99 067d7204815b7b2a819d7acc82527a5604819f79e1815b797d815b78a0067d7204815b7568 812674e9808474a1086009b40480f6749c812674b9815474ed04819b753e81bc75a381bc 760f0682b60481bc797481fb79eb82917a4508a10481f87ac281bc7b3381bc7be60682b304 81bc7f5681627fdf80b8802a094c0F> DC 42 /anglelfs4 <00832601808a748082bc8029028284802a03808b7a56038284748109b80380c2 7a560382bc802a09480F> DC 43 /anglerts4 <0083260180697480829a80290280a1802a09490382637a5603806a748109b703 829b7a560380a1802a0F> DC 44 /slashs4 <0084fe01802e748084cf8029028498802a03802e748109b80384cf802a0949 0F> DC 45 /backslashs4 <0084fe01802e748084cf802902802e802a038498748109b7038066802a0948 0F> DC 46 /slash <00832b018025792a830580290282cc802a038026792b09b9038305802a0947 0F> DC 47 /backslash <00832b018025792a8305802902805f802a09470382cc792b09b903805f802a 0F> DC 48 /parenlefttp <00836b01812d79218341802902830f802a0481917e25812e7c06812e798c0816 09e208e60481907aea81a47c4282077d990482507e9482b27f578342802a094d0F> DC 49 /parenrighttp <00836b0180287921823c8029028028802a0480b97f55811a7e9581637d9904 81c67c4281da7aea81da7988081a09e208ea04823c7c0481d87e26805b802a094d0F> DC 50 /bracketlefttp <00829b0181427921828f8029028142802a0678f809c10686c807810d08c007 7eb20F> DC 51 /bracketrighttp <00829b01800a79218158802902800b802a084007810d06793809c006870807 7eb30F> DC 52 /bracketleftbt <00829b018142792a828f803302814280330678f807814e08c1077ef30686c709 3f0F> DC 53 /bracketrightbt <00829b01800a792a815880330281188033067939077ef3083f07814d06870809 400F> DC 54 /bracketleftex <00829b0181427d6a818380330281428033067d3809c10682c8093f0F> DC 55 /bracketrightex <00829b0181177d6a815880330281188033067d3809c00682c809400F> DC 56 /bracelefttp <0083790181867c7082d4800002829d80000481da7f6381867f1581877e0c06 7e6509ea0681a40481f17ef082317f5382d47fd808a809490F> DC 57 /bracerighttp <0083790180a37c7081f180000280a4800008580481497f5181867ef281877e15 067e5c09ea06819b0481f17f15819e7f6380db800009490F> DC 58 /braceleftbt <0083790181867c7a82d480090281878009067e660481867d6681da7d18829d 7c7a09b708a904822e7d2a81f17d8781f17e660681a309160F> DC 59 /bracerightbt <0083790180a37c7a81f180090281878009067e5d0481867d8881497d2a80a4 7ca3085709b704819f7d1a81f17d6481f17e6f06819a09160F> DC 60 /braceleftmid <0083790180a3790a81f180090281878009067e540481867d7e814a7d2280a4 7c9a08610481497bf481867b9581877ab8067e5309ea06819b0481f17ba281a87bf580ec 7c8a0481a97d2181f17d7181f17e6f06819a09160F> DC 61 /bracerightmid <008379018186790a82d480090281878009067e660481867d7381d07d20828c 7c8a0481d07bf681867ba181877aa6067e6509ea0681ad0481f17b9382317bf682d47c7b08 9f04822e7d2181f17d7e81f17e5d0681ac09160F> DC 62 /braceex <0083790181867ed381f180090281878009067ecb09ea06813509160F> DC 63 /arrowvertex <00829b0181367d9d816480000281368000067d9e09ae06826209520F> DC 64 /parenleftbtex <00836b01812d792a8341803302812e8033081604812e7e61814d7cfd81c27ba5 0482167aae827779f9830f792b09b30482ae7a0482527aba82077bbd0481a37d1781907e68 81907fce08e5091e0F> DC 65 /parenrightbtex <00836b018028792a823c80330281da8033081b0481da7e6b81c67d1381637bbd 0481187ab980bc7a058028792b09b30480f379f981547aae81a87ba504821c7cfb823c7e62 823c7fc908ea091e0F> DC 66 /parenleftex <00836b01812d7d6a8190803302812e8033067d3809e20682c8091e0F> DC 67 /parenrightex <00836b0181d97d6a823c80330281da8033067d3809e20682c8091e0F> DC 68 /angleleft <0082ee01808a76d582798029028241802a03808b7b8003824176d609b80380c3 7b80038279802a09480F> DC 69 /angleright <0082ee01807476d5826380290280ad802a094803822b7b8003807576d609b803 82637b800380ad802a0F> DC 70 /unionsqr <0083410180377c1f83097ffa0280787fd90B80aa3faa4080067c670B7f688660 a0600782910B9380a18da1a00683990B7faa3faa3f80067c88077daf0683780F> DC 71 /unionsqrdsp <0084570180377a94841f800002808b7fd70B80b52cb52d80067aea0B805f8954 ac5407838f0B9b80ad92adac0685160B80b52bb52c80067b10077cbf0684f00F> DC 72 /integralcon <0081d80180387ba8826c800002822f7fd20B5a705736832d0Bb773c9b1acd604 823a800381f4800d81c17ff204815b7fbb81537ef681467e9004807e7e7680607d6a8122 7d2004811e7ced81197cbb81137c8804810d7c52810d7c0d80e77be10B625d2f500c710B9b 95acc387d60B5c923972404e0480457bb5808b7ba180c47bac0481567bc9815f7ca1816e 7d1704823e7d3182597e4681937e8a04819a7ed1819f7f1881a67f5f0B84a68adaa7f60B9e 9ec89de27d0281417e620481387e06812e7daa81277d4d0480a27d8a80b37e3f81417e6202 818f7e5c04821b7e2382097d6781737d4504817e7da281877dff818f7e5c0F> DC 73 /integralcondsp <00822c018045774983b8800a0283787fdc0B4f774c3c6d280Ba768e385cfcd04 83a18017832e801d83007fe50482977f6982387d7182147cba0481967cba812e7c6b810b 7bef0480f57ba181087b5081347b0e0481577ada817b7ac381b37aad0481967a0f814f781e 8101779d0B685737300a550Ba798a6c88adc0B569e19713b2d0B8d66ab5ac6530Ba277c47e e19104814c7796817378028190785e0481ca791881ec79d982127a980Ba683c989ec9804 82c97ad183057b12831a7b6204832f7bae83217c0282f57c440B60b034cd02e60482967d55 82b37e0082d57eab0482e37eef83047f90831d7fca0B8fa3c5b9db9202820d7c8f0481f1 7bfb81d67b6881bb7ad50480cc7b3781207c96820d7c8f02826d7c7d0483517c1583147ad7 821a7ac20482367b5682527be9826d7c7d0F> DC 74 /circledot <0084570180377c18841f800002822c800004811b800080387f1e80387e0d04 80377cff811e7c19822c7c1904833d7c1984207cfb84207e0d04841f7f2183408000822c 800002822c7fc004831a7fc083de7efb83df7e0d0483df7d1f831a7c5a822c7c5a048142 7c5a80787d2380787e0d0480787ef981407fc0822c7fc002822c7e520481d17e5281d27dc8 822c7dc80482867dc882877e53822c7e520F> DC 75 /circledotdsp <0085ea0180367a8585b280000282f58000048175800080377ec080377d4304 80377bc9817c7a8682f57a850484757a8685b37bc285b27d430485b27ec58479800082f5 80000282f57fb204844e7fb285637e9b85637d430485637beb844b7ad582f57ad40481a5 7ad580877bf380867d430480867e9781a27fb282f57fb20282f47d9f0B5080255525240B81 51ad25db250Bb180dcabdcdb0B81b257dc24dc0F> DC 76 /circleplus <0084570180377c18841f800002822c800004811a800080377f2080387e0d04 80387cfe811d7c19822c7c190483407c19841f7cfa84207e0d0484207f2383428001822c 800002820b7fbe067e6f077e6d04808c7e9880a97ef280f97f420481447f8c81a37fb5820b 7fbe02824c7fbe0482b47fb583137f8c835e7f420483b07ef083ca7e9983df7e2d077e6d06 81910280787ded078193067e6f0481a07c6681477c8b80f97cd80480a67d2b808d7d808078 7ded02824c7ded0781930483ca7d8083b17d2b835e7cd80483117c8b82b67c66824c7c5c06 81910F> DC 77 /circleplusdsp <0085ea0180367a8585b280000282f4800004823c800081897fb981077f3604 80857eb480377dfb80377d430480387bc781787a8782f47a860484757a8585b27bbf85b2 7d430485b37eca847b800182f480000282ce7fb0067dbb077db60480a27e0880c77e88813e 7efe0481ab7f6a82377fa582ce7fb002831c7fb00483b37fa5843f7f6a84ab7efe048522 7e8785477e0885657d6b077db70682450280847d1d07824a067dbb0482317ae681b17b18 813e7b8a0480c67c0280a27c7f80847d1d02831c7d1d0782490485477c7e85257c0484ab 7b8a0484377b1783ba7ae7831c7ad80682450F> DC 78 /circlemultiply <0084570180377c19841f800002822c8000048119800080377f2080387e0d04 80387cf781167c1b822c7c1904833c7c19841f7cfd841f7e0d04841f7f1b833a8001822c 80000283457f5603822a7e3b03810d7f580481647f9381be7fc0822b7fc00482957fc082f5 7f9883457f560280e07f2a0381fc7e0d0380e17cf204809e7d4380777da080777e0c048077 7e7c80a37ed180e07f2a0283727f280483b57ed883dc7e7983dc7e0f0483dc7d9883b27d4e 83747cf10382577e0d0383727f2802822a7de00383467cc30482e97c8482a07c5b82287c5b 0481ba7c5b81627c80810f7cc503822a7de00F> DC 79 /circlemultdsp <0085ea01803a7a8685b580000282f880000481768000803b7ec6803b7d4504 803b7c8f80847bd581057b540481867ad282417a8882f87a870484777a8685b57bc685b5 7d440485b57ebe8472800282f880000284917f150382f67d7b0381587f190481da7f718253 7fb382f87fb20483917fb2841e7f7884917f150281217ee20382bf7d450381257ba90480bf 7c2180887ca180887d420480877deb80c87e5e81217ee20284c77edf04852b7e6d85637ddf 85637d460485637c9b85257c2c84ca7ba703832c7d450384c77edf0282f57d0e0384937b70 04840e7b14839f7ad682f37ad60482507ad781d47b0f815b7b730382f57d0e0F> DC 80 /summation <0084200180397c1883e380000280398000085c0381a07ded0380397c31086807 83590383e27d1309660483b17cdd83977cb483667c910483177c5b82b27c5382557c5307 7e350381f17e0e0380a97fd30781890482e07fd383777fbd83c97f14099b038397800007 7ca20F> DC 81 /product <0083b00180377c1883798000028038800008530Bbd81e569e525067d2a0B803b 59241b25085207812308ae0B427f1a961adb0683310781c6067ccf0B803c58241a25085207 812408ae0B427f1a971adb0682d60B80c4a8dce6db08ad077cbf0F> DC 82 /integral <0081d80180387ba8826c800002822f7fd20B667559556b3c0B9563c76ed08f04 82817ff181fa801e81b27fe904815f7fa981597f20814c7ec20481337e15812c7d678119 7cba0481137c82810f7c4a81017c140B7a666a4d543c0B60693a671e820Bb5aa97ee5fd704 80187c1180457ba980a37ba90480ff7ba981307bed81497c3e04815c7c8181647cc8816d 7d0d04817a7d7981867de581907e520481987eaa819c7f0281a57f5a0B85a78adea8fb0B9e 9ec89de27d0F> DC 83 /union <0083410180377c1f83097ffa0280787fd90B80aa3faa4080067dde0480377d68 80427d1a806a7cd40480a97c6581227c2081a17c2004821f7c20829b7c6582d97cd4048300 7d1a830a7d69830a7db70682220B7faa3faa3f80067dde0482c97d7382c27d31829f7cf404 826b7c9a82097c6181a17c610481397c6180d37c9980a07cf404807f7d3180787d748078 7db70682220F> DC 84 /intersection <0083410180377c1f83097ffa02830a7e6304830a7eb183007f0082d97f4604 829b7fb5821f7ffa81a17ffa0481227ffa80a97fb5806a7f460480427f0080377eb28038 7e63067dde0B7f55c055c0800682220480787ea6807e7ee980a07f260480d37f8181397fb9 81a17fb90482097fb9826c7f80829f7f260482c27ee982c97ea782c97e63067dde0B8055c0 55c1800682220F> DC 85 /unionmultiset <0083410180377c1f83097ffa0280787fd90B80aa3faa4080067dde0480377d68 80427d1a806a7cd40480a97c6581227c2081a17c2004821f7c20829b7c6582d97cd4048300 7d1a830a7d69830a7db70682220B7faa3faa3f80067dde0482c97d7382c27d31829f7cf404 826b7c9a82097c6181a17c610481397c6180d37c9980a07cf404807f7d3180787d748078 7db70682220281be7ee80B80ab3fab3f80067f5f077f600B5581554080400780a0067f5f0B 8154c154c1800680a10780a10Bab80abc080c0077f5f0680a10F> DC 86 /logicalor <0083410180387c16830980000281c17fe80B759f4aa03f8003803c7c450B7052 ad40bc6b0381a17f7e0382c97c300B8f55cc67bd950381c17fe80F> DC 87 /logicaland <0083410180387c16830980000280787fe80B71aa3497446c0381807c300B8c5f b55fc1800383067fd40B8eab52bf43940381a17c9a0380787fe80F> DC 88 /summationdsp <0085a40180377a78856d80000280388000085c03824a7d020380387a8d086b07 84b703856d7bca096004852d7b86850c7b5384ca7b2904844c7ad983a27ad783127ad707 7da80382c77d430380ee7fce0782310483a47fce84347fc984ac7f8a0484f77f6285217f2e 854b7ee609a20384f48000077b440F> DC 89 /productdsp <0084fe0180377a7884c68000028038800008400480907fc280de7fa780de7f3f 067bfb0480de7ad180917ab880387aba083e0781e108c20481bf7ab881727ad181727b3a06 8486078219067b7a04838b7ad1833f7ab882e57aba083e0781e108c204846c7ab884207ad0 84207b3a0684050484207fa7846e7fc284c67fc008c0077b720F> DC 90 /integraldsp <00822c018045774983b8800a0283787fdc0B5f7a51605c400B8b60b259cd690B a4959bd380ec048379801383308016830a7ff00482b17f9582637e3682477db50481f27c24 81ae7a8a816378f504815478a4812a77a780db77710B666e496c30810480d0779e808e77fb 805777ca04801f77998070772f80d6774f0481477773817e781d819a78810481c8792181e9 79c482087a6804823b7b6e826d7c75829d7d7d0482a67db082fb7fa983277fdb0B9699bfa1 d1810F> DC 91 /uniondsp <0084570180377a94841f800002808b7fd70B80b52cb52d80067cf30480377c5c 80477bf0807e7b8f0480d57af6817b7a95822b7a950482db7a9583867af583dc7b8f048413 7bf0841f7c5c84207cca06830d0B80b52bb52c80067cf20483cc7c6783c57c1283927bba04 834a7b3c82be7ae8822c7ae804819b7ae8810c7b3b80c57bba0480987c0c808b7c6c808b 7cc906830e0F> DC 92 /intersectdsp <0084570180377a94841f80000284207dcc04841f7e3a84137ea683dc7f0704 83867fa182db8000822b800004817b800080d57fa0807e7f070480467ea680377e3a8038 7dcc067cf30B7f4cd347d38006830e04808b7e2a80977e8a80c57edc04810c7f5b819b7fae 822c7fae0482be7fae834a7f5a83927edc0483c57e8483cc7e2f83cc7dcd067cf20B804cd3 47d48006830d0F> DC 93 /unionmultdsp <0084570180377a94841f800002808b7fd70B80b52cb52d80067cf30480377c5c 80477bf0807e7b8f0480d57af6817b7a95822b7a950482db7a9583867af583dc7b8f048413 7bf0841f7c5c84207cca06830d0B80b52bb52c80067cf20483cc7c6783c57c1283927bba04 834a7b3c82be7ae8822c7ae804819b7ae8810c7b3b80c57bba0480987c0c808b7c6c808b 7cc906830e0282537e820B80be2cc02d80067f1c077f1c0B4381402d802d0780e4067f1c0B 8044d33ed3800680e40780e40Bbe80c0d480d3077f1c0680e40F> DC 94 /logicalordsp <0084570180377a92841f800d0282557fee0B72a83aaa2c8003803c7ace0B6a44 bb2dcf6503822c7f640383cc7ab30B9448e45fcf9b0382557fee0F> DC 95 /logicalanddsp <0084570180377a92841f800d02808b7fee0B6db71ca131650382017ab30B8f55 c556d48003841b7fd30B95bb45d2319b03822c7b3e03808b7fee0F> DC 96 /coproduct <0083b00180377c1883798000028038800008530Bbd81e569e525067d2a0B803b 59241b25085207834108ae0B427f1a971adb0682d60B80c4a8dce6db08ad077edc08530Bbe 81e669e625067ccf077e3a0683310B80c4a9dce6db08ad077edd0F> DC 97 /coproductdsp <0084fe0180377a7884c680000280388000083f0480907fc180de7fa780de7f3f 067bfb0480de7acf80927ab880387aba083e07848e08c204846c7ab884207acf84207b3a06 84050484207fa7846e7fc184c67fbf08c1077e1f083f04833e7fc1838b7fa7838b7f3f06 7b7b077de70684850481727fa781c07fc182197fbf08c1077e1f0F> DC 98 /circumflex <00822c017ffc8230823082e702811582e8037ffc82470A8d6903811582af03 822282300A8e9703811582e80F> DC 99 /circumflexwide <0083e8017fff823e83e983060281f48307037fff82580A84670381f482ce03 83e5823f0A84990381f483070F> DC 100 /circumflvrywid <0085a4017ffc824085a883070282d28307037ffd825a0A86660382d282cc03 85a182400A879a0382d283070F> DC 101 /tilde <00822c0180018260822a82d602821c82d60481c7828f817e8272811982b104 80a682fb805c82be800282720A8d6e04805d82a580b182c5810e828504817d823b81d5827b 822a82c70A728f0F> DC 102 /tildewide <0083e8018000826483e182f10283d682f204832f829f82a7826d81f182bb04 8132830d80ac82cf800082760A886f0480b082b1812582e581db82960482a1824183318280 83e282e00A74920F> DC 103 /tildevrywide <0085a4018000827885a482fe02859e82fd0484ad82ae83ea827b82f082d004 827a82f982018308818582f60480ff82e2807f82bb8000828c0A886c0480f982cd81da8307 82d482ad048353828083d48275845a828c0484cd829f853982bf85a482ee0A7a8f0F> DC 104 /bracketfls2 <0081d80180de792a81c580290280de802a0679010780e808b8077f5006869007 80b008b7077f180F> DC 105 /bracketrts2 <0081d8018012792a80fa8029028013802a08490780af067970077f51084807 80e70686ff077f190F> DC 106 /bracketlfbts2 <0082100180de792a81fd80330280de80330678f807811f08b8077f190686d009 480F> DC 107 /bracketrtbts2 <008210018012792a813180330280fa8033067930077f19084807811f06870809 480F> DC 108 /bracketlftps2 <0082100180de792181fd80290280de802a0678f809b80686d10780e708b707 7ee10F> DC 109 /bracketrttps2 <008210018012792181318029028013802a08490780e706792f09b806870807 7ee10F> DC 110 /bracelfs2 <00829b018075792a8234802902820d802a0481d28019819a8005816c7fdc04 81307fa681287f7681287f2a067e780481287d1880e87cf180757cb908640480e87c658128 7c3c81287bb4067e7804812879d7813179a88178796f0B9a6bb85bd7500Ba871bc6ce66c08 9e0481b27969817279a481727a330681670481727be6816b7c1d81357c570B5da532bd06d4 0Bac97d7aefad304816b7d3881727d6f81727dbc0681660481727fb081b37fed8235800c08 9e09580F> DC 111 /bracerts2 <00829b018065792a82258029028066802a08620480e87fed81287fb081287f22 067e9a0481287d70812f7d3881667cfe0Ba25bce43fa2d0B54692851062c04812f7c1e8128 7be681287b9a067e9904812879a480e979698066794908620B8d809a80a8800B9285a38bb5 910B9e89b998d3aa048167799f817279d081727a2c0681880481727c3b81b47c6682267c9d 089c0481b27cf181727d1981727da20681880481727f7e81697fae81237fe60480ee8010 80a9802a8066802a0F> DC 112 /radicals1 <0083e80180667b80840e80390283db80390381cd7be80380f87de20380667d72 0A916b0Ac9ba0381a47b8009aa03840e8039094d0F> DC 113 /radicals2 <0083e80180667926840e80390283dc80390381cb79bb0380f87cb50380667c0d 0A926c0Ac7d50381a2792609a903840e8039094e0F> DC 114 /radicals3 <0083e801806676cc840e80390283de80390381c9778e0380f97b880380667aa8 0A946d0Ac4f003819f76cd09aa03840e803909500F> DC 115 /radicals4 <0083e80180667472840e80390283df80390381c775620380f97a5b0380667943 0A956e0380bd79bb03819d747309aa03840e803909510F> DC 116 /radicalbtex <008420018073790182e980170282bb80170679eb0381007f5f0380737e4c0A92 6e0380d47edb0382be790109ab06871609520F> DC 117 /radicalex <0084200182ba7d8682e980170282bb8017067d7009ae06829009520F> DC 118 /radicaltpex <0084200182ba7d868436802e0282bb802e067d5909ae06827907814e08ae07 7e840F> DC 119 /arrowdblvertex <00830a0180fc7d9d820980000280fc8000067d9e09af06826209510281db8000 067d9e09af06826209510F> DC 120 /arrowupex <00829b0180657d9d8234800002814d80000481077fa180d97f6b80667f450850 0480c47f2d80f47f5681367f9d067e0109ae0681ff0481a57f5781d77f2d82357f1508b004 81c07f6c81947fa0814d80000F> DC 121 /arrowdownex <00829b0180657d9d823480000281368000067e020480f97e4480be7e738066 7e8a08500480d47e35810a7df9814d7d9e0481907df981c77e3682357e5a08b00481dc7e73 81a27e4481647e020681fe09520F> DC 122 /bracehzlfdnex <0081bc017fee7f3181cf806a028197806a0480d2806a803f80077fee7f57085b 09b20480467f7c80787fac80c47fd204811c7ffe816f800081cf800008ea09480F> DC 123 /bracehzrtdnex <0081bc017fee7f3181cf806a027fee806a081604804280008094800080e37fdc 04813a7fb681727f84819d7f3209b208a50481a97fa981757fed812880200480c180658064 806a7fee806a0F> DC 124 /bracehzlfupex <0081bc017fee800081cf8139027fee8139085c04801480c0804580808094804b 0480fb80068158800081cf800008ea04817a806a8128806c80d9808f04808180b6804b80e6 80208139094e0F> DC 125 /bracehzrtupex <0081bc017fee800081cf813902819d813904817580ee814680c080f8809904 80a2806e804b806a7fee806a0816048053800080b58005810f803b04816c807181a380b6 81cf811508a4094e0F> DC 126 /arrowdblvttpex <00830a0180377d9d82d2800002818580000481567fb2812e7f7b80e97f3d04 80ad7f0780807eed80387ecf084f04808b7ec180b47ed980fc7f11067e8d09af0681a00B9f a2bdc4dae80B9c5eb93bd61a067e5e09af0681790482547eda827b7ec282d27e9e08b104 82327f1181dd7f6e818580000F> DC 127 /arrowdblvtbtex <00830a0180377d9d82d280000280fc8000067e8e0480bc7ec080827ee18038 7f01084f0480d17e9081317e2b81857d9e0481d97e2b82397e9082d27ed008b10482847ee1 824c7ebe820a7e880681780951067e5f0B635f463c2a1a0B63a445c626e806819f0951 0F> DC 160 /parenlefts1 <0081ca0180797b7d81a08029028186802a0481457ff9810b7fc680e17f7f04 80967efe807a7e68807a7dd404807a7d39809a7c9b80ea7c140481117bd381487ba78186 7b7d099b0481657baf81327bdf810f7c260480cc7cac80bc7d4180bc7dd40480bc7e6c80cd 7f0681147f8f0481367fd081687ffe81a1802a09650F> DC 161 /parenrights1 <0081ca0180297b7d81508029028045802a09650480627ffe80957fd080b67f8f 0480fd7f06810e7e6c810e7dd404810e7d4180fe7cac80bc7c260480977bdd80677bb0802a 7b7d099b0480847ba980b77bd080e07c140481317c9b81507d3981507dd40481507e688134 7efe80e97f7f0480bf7fc680857ff98045802a0F> DC 162 /bracketlfs1 <0081a10180c27b80818b80290280c2802a067b560780ca08b3077f6906844507 809708b2077f360F> DC 163 /bracketrts1 <0081a10180147b8080de8029028015802a084e078096067bbb077f6a084d07 80c90684aa077f370F> DC 164 /bracketlfbts1 <0081d80180c27b8081c380330280c28033067b4d07810108b3077f3206848009 4d0F> DC 165 /bracketrtbts1 <0081d80180147b80811580330280e38033067b80077f32084d0781010684b309 4d0F> DC 166 /bracketlftps1 <0081d80180c27b7681c380290280c2802a067b4d09b30684810780ce08b207 7eff0F> DC 167 /bracketrttps1 <0081d80180147b7681158029028015802a084e0780ce067b7f09b30684b307 7eff0F> DC 168 /bracelfs1 <0082470180577b8081f080290280587de208660Ba777d26ff3580Bad60af3daf 0b067f0d0480f97ba881757b8081f07b80089c04817b7ba781387bba81397c440680d204 81387d9f81067db9808c7dd50481077df281387e0a81397e950680d20481387ff1817b8002 81f0800e089c048176802a80f9800080fa7f72067f0e0B804e7d2b510b0B5f6934610d57 0F> DC 169 /bracerts1 <0082470180567b8081ef80290281f07de20B598a2d920ca90B54a051c351f506 80f204814d800180d3802a8057802a08640480cd8002810f7ff1810f7f67067f2e04810f 7e0a81417df281bc7dd50481427db9810f7d9f810f7d16067f2e04810f7bba80cd7ba78057 7b9c08640480d37b80814d7ba7814d7c380680f30B80b283d5aff50Ba197cd9ff4a8089a 0F> DC 170 /anglelfs1 <0081d80180607b80819c8029028162802a0380607dd50381627b8009ba03809b 7dd503819c802a09460F> DC 171 /anglerts1 <0081d801803c7b8081788029028077802a094503813e7dd503803c7b8009bb03 81787dd5038077802a0F> DC 172 /linevertex <00814d01808f7da280bd80330280908033067d7009ae06829009520F> DC 173 /linedblvertex <00822c01808f7da2819c80330280908033067d7009ae068290095202816e8033 067d7009ae06829009520F> DC 174 /slashs1 <0082470180247b80822280290281e8802a0380257b8009ba038223802a0945 0F> DC 175 /backslashs1 <0082470180247b808222802902805f802a09460381e87b8009bb03805f802a 0F> DC 176 /parenlfs2 <0082550180b27929822b8029028208802a0481b87fdb816f7f8a81397f2604 80d17e6280b27d8580b27caa0480b27bcf80d17af281397a2e04816f79c881b779798208 792909a40481df7978819e79c581717a2b0481177af480fd7bd080fd7caa0480fd7d848117 7e6081717f2904819e7f8d81e07fdd822c802a095c0F> DC 177 /parenrts2 <008255018029792981a3802902802a802a0480757fdd80b87f8d80e47f2904 813e7e6081587d8481587caa0481587bd0813e7af480e47a2b0480b779c580767978802a 792909a30480a0797b80e479c5811c7a2e0481847af281a37bcf81a37caa0481a37d858184 7e62811c7f260480e77f8a809d7fdb804d802a095d0F> DC 178 /parenlfs3 <0082e00180ea76d482b6802902828a802a04822a7fbc81d27f4b81907ec804 810c7dc380ea7ca180ea7b800480ea7a638109794b818878490481cf77ba8225774d828a 76d509ac0482587744820c77a781d27831048162793d813e7a60813e7b8004813e7c9c8161 7dbb81ce7ec40482067f4b82597fbc82b6802a09540F> DC 179 /parenrts3 <0082e001802976d481f68029028056802a09540480877fbc80da7f4b81127ec4 04817f7dbb81a27c9c81a37b800481a27a60817e793d810e78310480d477a780887744802a 76d509ac0480bc774e811077b8815878490481d8794d81f67a6181f67b800481f67ca181d4 7dc381507ec804810e7f4b80b67fbc8056802a0F> DC 180 /bracketlfs3 <0082100180f976d581ff80290280fa802a0676ac07810608bc077f360688dc07 80ca08bc077efa0F> DC 181 /bracketrts3 <00821001801076d581158029028010802a08440780ca067724077f36084407 8106068954077efa0F> DC 182 /bracketlfbts3 <0082470180f976d5823780330280fa80330676a307813d08bc077eff06892109 440F> DC 183 /bracketrtbts3 <00824701801076d5814d803302811180330676df077eff084407813d06895d09 440F> DC 184 /bracketlftps3 <0082470180f976cc823780290280fa802a0676a309bc06892107810108bc07 7ec30F> DC 185 /bracketrttps3 <00824701801076cc814d8029028010802a08440781010676df09bc06895d07 7ec30F> DC 186 /bracelfs3 <0082ee01809276d58279802902824b802a0481ad7ff181567f9081577ee106 7de30481567c2981187bd780937b8f08620481177b2a81567ad481577a3c067de1048157 77b98170776b81ba77260B9a68b854d9450Bb06cb36be66b089f0481e7772581ac778b81ac 78230681fa0481ac7ad681707b2680d57b800481707bdb81ac7c2881ac7ce30681fa0481ac 7f7181eb7fdc8279800a08a009520F> DC 187 /bracerts3 <0082ee01807576d5825b8029028075802a08600481067fdb81427f7381427edd 067e060481427c29817f7bdb821a7b800481807b2781427ad581427a1d067e06048142778c 81077725807576f508610B8f809f80ae800B9085a08cb0920B9e8cba9dd3b204817a7760 819777b18197781d06821f0481987ad581d87b2a825b7b71089e0481d67bd781987c298197 7cc406821d0481977f45817f7f9481347fda0B669848ab27ba0B589146961a960F> DC 188 /anglelfs3 <008263018053792a820080290281c7802a0380547cab0381c7792b09b903808d 7cab038200802a09470F> DC 189 /anglerts3 <008263018062792a820f8029028063802a0381d67cab038063792b09b903820f 7cab03809c802a09470F> DC 190 /slashs3 <00841401802a76d583ea80290283b2802a03802a76d609b90383ea802a0948 0F> DC 191 /backslashs3 <00841401802a76d583ea8029028063802a09470383b276d609b8038063802a 0F> DC /FontBBox {-18 -2958 1461 775} def end /Dutch801-Roman-DECmath_Extension bsd definefont pop %%EndFont %%BeginFont: Dutch801-Italic-DECmath_Italic % Bitstream Fontware PSO Font -- Version 1.6 % DECmath Font Version 1.0, created 4-13-89 % % Copyright 1989 by Bitstream, Inc. All Rights Reserved. % Copyright 1989 Digital Equipment Corporation % % This product is the sole property of Bitstream Inc. and % contains its proprietary and confidential information % U.S Government Restricted Rights % This software product is provided with RESTRICTED RIGHTS. Use, % duplication or disclosure by the Government is subject to % restrictions as set forth in FAR 52.227-19(c)(2) (June, 1987) % when applicable or the applicable provisions of DOD FAR supplement % 252.227-7013 subdivision (b)(3)(ii) (May,1981) or subdivision % (c)(1)(ii) (May, 1987). Contractor/manufacturer is Bitstream Inc. % /215 First Street/Cambridge, MA 02142. % % This software is furnished under a license and may be used and copied % only in accordance with the terms of such license and with the % inclusion of the above copyright notices. This software or any other % copies thereof may not be provided or otherwise made available to any % other person. No title to and ownership of the software is hereby % transfered. % % The information in this software is subject to change without notice % and should not be construed as a commitment by Digital Equipment % Corporation. % % BITSTREAM, INC. AND DIGITAL EQUIPMENT CORPORATION DISCLAIM ALL % WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED % WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL % BITSTREAM, INC. AND DIGITAL EQUIPMENT CORPORATION BE LIABLE FOR ANY % SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER % RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF % CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN % CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. % /n_chars 128 def /DC { /bits exch def /name exch def /num exch def num 256 lt {Encoding num name put} if CharStrings name bits put } bind def /bsd 15 dict def bsd begin /FontType 3 def /FontName /Dutch801-Italic-DECmath_Italic def /PaintType 0 def /UniqueID 440305 def /FontMatrix [.001 0 0 .001 0 0] def /FontInfo 12 dict def /CharStrings 1 n_chars add dict def CharStrings /.notdef <0F> put /Encoding 256 array def 0 1 255 {Encoding exch /.notdef put} for /temp 15 dict def temp begin /get-word { 0 s i get add 8 bitshift /i i 1 add def s i get add 32768 sub /i i 1 add def } bind def /get-byte { s i get 128 sub /i i 1 add def } bind def /get-name { /len s i get def /i i 1 add def s i len getinterval /i i len add def } bind def /eval-arr 16 array def eval-arr 16#00 {get-word 0} bind put eval-arr 16#01 {4 {get-word} repeat setcachedevice newpath} bind put eval-arr 16#02 {closepath 2 {get-word} repeat moveto} bind put eval-arr 16#03 {2 {get-word} repeat lineto} bind put eval-arr 16#04 {6 {get-word} repeat curveto} bind put eval-arr 16#05 {4 {get-word} repeat get-name do-char} bind put eval-arr 16#06 {0 get-word rlineto} bind put eval-arr 16#07 {get-word 0 rlineto} bind put eval-arr 16#08 {0 get-byte rlineto} bind put eval-arr 16#09 {get-byte 0 rlineto} bind put eval-arr 16#0A {2 {get-byte} repeat rlineto} bind put eval-arr 16#0B {6 {get-byte} repeat rcurveto} bind put eval-arr 16#0F {end PaintType 2 eq {temp begin stroke exit} {temp begin fill exit} ifelse } bind put /do-char-arr 16 array def do-char-arr 16#00 {get-word pop} bind put do-char-arr 16#01 {4 {get-word pop} repeat} bind put do-char-arr 16#02 {closepath 2 {get-word} repeat moveto} bind put do-char-arr 16#03 {2 {get-word} repeat lineto} bind put do-char-arr 16#04 {6 {get-word} repeat curveto} bind put do-char-arr 16#05 {4 {get-word} repeat get-name do-char} bind put do-char-arr 16#06 {0 get-word rlineto} bind put do-char-arr 16#07 {get-word 0 rlineto} bind put do-char-arr 16#08 {0 get-byte rlineto} bind put do-char-arr 16#09 {get-byte 0 rlineto} bind put do-char-arr 16#0A {2 {get-byte} repeat rlineto} bind put do-char-arr 16#0B {6 {get-byte} repeat rcurveto} bind put do-char-arr 16#0F {closepath exit} bind put /eval { /s exch def /i 0 def { /t s i get def /i i 1 add def eval-arr t get exec } loop } bind def /do-char { t s i matrix currentmatrix 2 {6 index} repeat translate 2 {8 index 256 div} repeat scale end CharStrings 5 index get temp begin /s exch def /i 0 def { /t s i get def /i i 1 add def do-char-arr t get exec } loop setmatrix [/i /s /t] {exch def} forall 5 {pop} repeat } bind def end /BuildChar { exch begin 0.2 setflat Encoding exch get CharStrings exch 2 copy known not { pop /space } if get temp begin eval end end } bind def FontInfo /version (Fontware-PSO 1.6) put FontInfo /OutlineResolution 1000 put FontInfo /Copyright (Copyright 1989 by Bitstream,Inc. and Digital Equipment Corp. All Rights Reserved.) put FontInfo /Notice (Dutch 801 is a registered trademark of Bitstream, Inc.) put FontInfo /Date (1989/4/13 12:34:32) put FontInfo /FullName (Dutch 801 Italic DECmath_Italic (TM)) put FontInfo /FamilyName (Dutch 801) put FontInfo /Weight (Medium) put FontInfo /ItalicAngle -15.60 put FontInfo /isFixedPitch false put FontInfo /UnderlinePosition -108 put FontInfo /UnderlineThickness 60 put 32 /psi <008286017fe97f24825b82560280de8013048022804280c3811880bd818f0B7eb2 50d51fc704802281c57fff81887fe981530A97770B8fa0a1c2bfd60B958eab88ab6c048068 8151803680f78031809f04802e806c8049803d8071801d0B9d69bf60e4590380967f2509df 0381237ff40481ba800b821480848244810e0482528136828081d9822781d60481d781d2 821381608215813904821a80ed81f780a581c5806f048199803d816b8021812b80160381af 825709610380de80130F> DC 33 /omega <0082ac017ffd7ff3826981d30280fb81b90A7f9a04803581b27fad80a6802f 80180B9e61cf54f9610Bb58fd3bcecea0B855a8f2fb51d0481787fe781b37ffb81dc801504 8276807b82b6819681e481d30A7469048224819782178151820a81040481fd80bb81d9801f 817b80170B647e498d3fa80481298070813a80a8814c80d604815a80f981ae81808158818a 04810d8192811a80f6811380cb048109808b80e6802c809f801a0B6c7b58834a910B669b67 c86ceb04805e80d9807181218090815d0B9bb6b3ccebdc0F> DC 34 /epsilon <0081b80180027ff3817181d702815480670A688e0B6555462d10240B4c761b 9412ca04805480a1808280dc80bd80e90B9e7de264e48f0B81a93e95299104805a812380a5 81d7810d81b50Ba3759c56a43b0B8964ad61bb7b0B96a56fcf4fde04810d81de80d081dd 80a081cd04802e81a680168129809180fc0B50741d620235047ff080748008801d804c8002 0480807fef80bf7fee80f380040Bad94c8bae1e30F> DC 35 /theta1 <008209017ff37ff5821382e702816981db04816881618166808d8106803404 80bf7ff38071801f8091808e0480a580d3810381a3809c81d004804881f5800c818e7ff3 814e0A97780B8c9cb3f0ddde0480918190804580c4803e80a204802c8044805d7fee80c5 7ff6048189800581bc812881c181c60B9a79b373cd6d0A85a20B65864a8d2f940481bd822a 81bd8272819782aa04816f82e6811482f980d482d804809182b5807e825a80b882240480e8 81f8812b81eb816981db0281698200048138820d80fc821a80dd82440B62a76de9a2f504 815b82cd8165823b816982000F> DC 36 /omega1 <0082f001800c7ff382e781cc02807e818709b00480738148803d8104803580ab 048030806b804b8019808b7fff0480e67fd78123801a814b8063048155801081817fe081da 7ffc04821d800f825a8047827880860482a380de829a8130826f818409ea0A8ec9077ddf04 805581cd802d81ca800d8152099e0B8ca7abb5d3b5028245818704824f8123823b80b6820a 805e0481f1803181b57ff981818027048143805f818980d781a2810e0B94aa8ce955db04 813e815a814980ca813e80960B774d4f161d060B4a6e2fa72ed404808780cc80b2813680dc 81870781690F> DC 37 /rhomath <0082230180037f2081dd81d702813a7f200A94880481587f9c80e77f8a8093 7f940480147fa3801f802b8027808a0480358051804c801e808580050480d97fe1813e8003 817d80400481ca808b81f6810181ce816a0481ac81c0814781e780f181d104807f81b3803a 814a801d80de048002807a7fed7fdf802f7f8604805e7f4880aa7f3e80f27f3f0B9f80b97f c8610280a9815c0480d1819c812c81e8816b81950481a2814b817380ae8146806704811c 802380bd7fe980868042048057808e807e811680a9815c0F> DC 38 /sigma1 <00816801800a7f99816f81da0280427fc40A78640Ba276c56ce8770Baa8cc7b0 d1da04810e8069809180ac805880f8048023813f8068819380b081a404811181ba81258175 815681850Bab8eaad245d60480e081dc80a881d1807681b204804081918012815c800c811c 047fff80898083807080ac80110B8c6687456c350B667045782a7e0F> DC 39 /phi1 <00826c017ffe7f1d823381da0280947ff90380557f1d09d60380e87ff404812c 7ff681668005819f802c0481f68069823c80d58233814304822a81b081c58201815b81c804 8108819c80ec812a80d580d70380a280240480628041804f8083805380c60480588116807a 815980af81930A6b96048046816a7ff8811f7fff80ac048003804e8040801480947ff902 811f80bc04813281008144815d819081790B9c8abb81ce6b0B9668954491260481e680c4 81c58083818e8056048160802f812c801f80f1801a03811f80bc0F> DC 40 /arrowlefttop <0083e801803e811283a981d00283a9811308b8077d03038179819e0A6ab303 803f8155083e07836a0F> DC 41 /arrowleftbot <0083e801803e808c83a9814b0283a9814b077c96083e038163808d0A96b303 80ac81120782fd08b90F> DC 42 /arrowrighttop <0083e801803e811283a981d002803f811307836a08c203828581d10A6a4d03 833c814b077d0308480F> DC 43 /arrowrightbot <0083e801803e808c83a9814b02803f814b08470782fd03826f80c00A964d03 83a9810908c2077c960F> DC 44 /hookleft <00811601809a81128169826b028169814b04811a814680d2816780d581c204 80d8821a811e82358169823208b90B57812c7e08690480bd8237809b81fa809b81bf04809b 818480bd814880f1812a0Ba46bce67f86908b80F> DC 45 /hookright <008116017fbc81128089826b027fbc814a08490Baa7ed382f8970480688148 80898184808981bf04808981fa80688237803482540B5b953298089708470480078235804c 821a804f81c20480528166800a81477fbc814a0F> DC 46 /triangleright <0081f4018011800081e281cb02801281cb067e350381e280e503801281cb02 803e818803818480e703803e80470681410F> DC 47 /triangleleft <0081f4018011800081e281cb0281e281cb03801180e50381e280000681cb02 81b68188067ebf03807080e70381b681880F> DC 48 /zerooldstyle <00820201801a7ff281e6820a02802a816204800480ea80238042809d800704 81247fc781b4801381db80a40481fc812081de81c7815a81fc0480d6822f805481e3802a 816202807a814e048091823d8190822d818a80c9048189809681848058815e803204813e 80128107800880de801c048082804a807180f6807a814e0F> DC 49 /oneoldstyle <00820201807d8000818481fd02807e81e80Bd57bd767d715067f030B802f7e19 2915086b07810608950B2b84289a28eb0680fd0B80d283e7d8eb0895077efa086b0F> DC 50 /twooldstyle <008202018026800081e0820a028027801908670781850381e1808e09630481a6 80528175805181388051077f610480e28088813980c3817681070481ae814781ba81a48175 81e104813e821180eb821780ad81f004807e81d2806481a1804f816f0A9a790B97a3b3c2dd ce0Baf8ee67ffd5204815f8150813a8113811480ea0480cd809c8078805c80278019 0F> DC 51 /threeoldstyle <0082020180277f3c81c6820a0280a580b7086b0480f280a181488095816c8047 04818c800081747fa481337f790480bf7f2b80a97fae804d7fa90B547d53487031048072 7f3080cf7f39810b7f4a0481767f6a81c57fc381c680350481c68096819680c8814080e80B a4a1cbc4daf40481ad819a819281d6815b81f5048120821880ce820e809681e904806781ca 8049819a803381670A91740B96a1adc2d2d50480c681c8810681cb812f81a404815d817a 815481308132810204810f80d280dd80bf80a580b70F> DC 52 /fouroldstyle <0082020180267f3c81e4820a0281357ffa067f4209ce0680be09e108c3091f06 81cd09530380278046083407810e028135819b067ea2077f17038135819b0F> DC 53 /fiveoldstyle <00820201802a7f3c81d182190280c281fe03804d80f10480b680e9813980d1 816a806804818f801b817b7fb581377f800B676d476327650B6a82598f489d0B67953fb01c a20B5b70694583320480847f2980fd7f3d813b7f5f0481a97f9d81dc802881ad809e04817f 810d810681388099814b0Aace40780e20Aabe20A73890B6d6560644064077f3d0F> DC 54 /sixoldstyle <00820201802f7ff381d982c0028093815f0480c58197810e81ab8147816e04 8183812d818880a1816a805104813d7fd280597fe58093815f0281c382ab089604817482b7 812982a780e6827b04808b8240805181e4803b817b048027811c802480a5805c805004808c 800780e57fe6813b7ff90481d38017820080ea81b8816204817881cd80fa81cf809d818c04 80c482388115828a81c382ab0F> DC 55 /sevenoldstyle <0082020180257f3d81e981fd02806781fd0380268153099704806381a8807a 81a880d381a90780bf0380bd7f3d09be0381ea81fd077e7d0F> DC 56 /eightoldstyle <00820201802d7ff281d382c10280d98152048113812c817d80eb818680a104 818f804c815a800d8104800e04804f8010804f810580d98152028132818404816d81a581af 81c981bb82130481ce8288817082c1810782c104808f82c080308269804881ed04805481ac 808c818180c0815e048081813e803e8110803180c404801b8044807f7ff480f97ff3048173 7ff281eb804d81d080d20481bf8127817281558132818402811e81910480eb81b0809b81de 808d821d04807d826a80b782a7810382a80481a182aa819d81de811e81910F> DC 57 /nineoldstyle <00820201802b7f3c81d5820a0280427f53086a0480937f4780d97f55811f7f83 04817a7fbe81b4801981ca80820481dd80e181e1815881a981ac04817981f6811f821780ca 820504803381e680038113804c809b04808e8030810a802d816880710481578026813b7fe1 81037faa0480cc7f75808b7f6080427f53028171809e048140806680f6805280bd808e04 808080cf807d815c809981ac0480c7822a81aa821b8171809e0F> DC 58 /periodmath <0080fa0180427ffa80b7806d02809a80650B3fa60443461d0Bc15afcbdbae3 0F> DC 59 /commamath <0080fa0180277f5980d280720280287f6e0A876b0Ba593c7a8e4c60Ba1a3bbcd bffc0B87dc1ff70bae0B6f40b945b71d0B7e4d3c1f14080F> DC 60 /less <008341018080801e82bf82360282c08236038081814a08410382c0801f08cb03 80e7812a0382c081eb08cb0F> DC 61 /slashmath <0081f40180377f1481bc82fb02819082fc0380387f1509aa0381bc82fc0954 0F> DC 62 /greatermath <008341018081801e82c082360280818236083503825b812a038081806a0835 0382c0810b08bf03808182360F> DC 63 /starmath <00822501800f8019821481fc028151814403811281fd0380d48144077f3c03 80b080d40380798019038112808d0381ac801903817580d40382158144077f3c0F> DC 64 /partialdiff <0081f40180417ff481b7827b02816981200481508166811a818c80cd 8177048045815380118085807180210480997ff780d87fe9810e7ffe048166801f81928086 81a680da0481c4815681cd8268811b827a0B558412720c3e0B7c51b657cd6e0B9c9bbacfe3 a4048185821b817781618169812002808f80c1048099810280be816e8115815b0481638149 815c80e1815280a4048147806481277ffc80d1800b04807f801980868084808f80c1 0F> DC 65 /A <008263017f998000822582a302817682a3096a03800a805e0B614a4f3a14330A7c6f 0780d50A85910B3b8031a551df0Ab5e20B8487898e918e0780d70A930c0B8a3f742433250A 7c6f0780fe0A84910B3d8438a42fdf03817682a302815b8103077f3d03812f820503815b 81030F> DC 66 /B <008263017fd08000823d82940281678294077f110A7b6d0Bc879d06bbd22038038 80670B6d3a61311d2c0A7b6d07811d0481228000815780058188801a0481c2803481f88065 820780a504821280d3820a810681f0812d0B6d9d4eac2fb80481f7817f824d81bd823b8224 04822a828781b982948167829402811c823d0B8eb798b6cfb70481bf827581e5823381d0 81e40481b7818781678170811181700B6e80527c599603811c823d0280d6813c0B889eb394 c894048190815081b580f78192809304817180348113801680b7801f0B56835ca565c403 80d6813c0F> DC 67 /C <00829b0180247ff2829582a2028296829c09670B71676066456f04819f82c48102 828a8091820804804881b480198146802780d5048033806f8073801b80d7800004812a7fe7 818d7ff181d8801d0Bab9bcebeeee40A6b930481657fa78050802a80a9816c0480fe829f 826b82f2825581d90999038296829c0F> DC 68 /D <0082d2017fcf800082aa82940281778294077f020A7a6d0Bc979d36abf2203803b 80670B6e3c5d2e192c0A7b6d07811f04813a80008186800b81ca802d04823b8065829480d2 82a681510482c48220823782948177829402811682260B8fb895d1d5cf0481a3827381db 82698203823d04824381f7823f8189822b8133048201807e8185800980c780220B438850ac 5edd03811682260F> DC 69 /E <008263017fce8000825682940282578294077e200A7b6d0Bc979cc68b922038033 80670B6e3a6431212c0A7b6d07820603821880b5096d0481d1805881a1802b8133802304 8114802080b38018809a802b0B6b8f7db982cc0380d781510481508151817a8165816a80e5 09930381bf81cf096d0B77686f4f5b3c04815d81658112817180df817103811482330B8593 8ab09cbc048143827b81a5827481b282740Bde7ff773f611099203825782940F> DC 70 /F <008263017fd88000827482940282748294077e0b0A7b6d0Bc97ad96cc522038048 80670B6d395b31162c0A7b6d0781290A83910B47811a8a2dce0380f0814d04810c814d817c 81588193813a0B94688d408a2409930381ef81ce096d0B7467674c503a0481808166812d 816e80f8816e038129822f0B859489b5a0be048169827981b8827381d582730Bda7ef15bf0 05099203827482940F> DC 71 /G <0082d20180217ff282ba82a30282ba829b09660B71696252435b0B77836e89658d0B 668d4b962e9b04819082b08127828f80d682500480758205802f818f8023811504801980b4 8043804c809980180481107fd181b27ff28225803303824d80d00B92c397dde1e10A859107 7ef80A7b6f0Bc47bdb7dc7310381c9805b0481a57fdc80647fe3809b812c0480de82ba825e 82eb827081d1099b0382ba829b0F> DC 72 /H <0082d2017fcf80008303829402817e8294077efa0A7b6d0Bc879cf69bc22038038 80670B6c3a61311d2c0A7b6d0781050A86930B3786309843de0380d381380B85908b949d94 0780eb0B98809f7b98620381bd80670B6e3a63311e2c0A7b6d0781050A85930B3886319844 de03829b822d0B91c0a1d3e3d40A8593077efb0A7b6d0Bc979ce69bc2203820b81850B7c70 756b646c077f140B6a7f6186689e038115822d0B91c0a2d3e4d40A85930F> DC 73 /I <00814d017fd18000817c829402817d8294077efe0A7a6d0Bc979cc68b922038036 80670B6d3b6531212c0A7b6d0781010A86930B3786359a47de038117822d0B91bf9fd3e0d4 0A86930F> DC 74 /J <0081bc017fb87ff381d3829402808e806d0B7864723e582c0B6e734f703c7d0B6e8b 799a7baa0B849c78b75bbd0B3690292970060480187feb80617fec809280040480d98029 80f78077810a80c003816b82350B90bea6cae4cc0A8593077ee20A796c0Bd87be572cf1b03 808e806d0F> DC 75 /K <00829b017fd2800082db82940281888294077ef10A7b6d0Bc97ad56ac22203803f 80670B6d3a5c30192c0A7a6d07811a0A86930B3a841e8b33d70380dd813e0B848e90919985 03818a80710Bae3fa82257210A7b6e0781230A85920B478327a207d003814881770381ed 81f7048220821e8252824a828b826b0B988eae95ca970A8792077f120A7a6d0Bdf7fb94c83 220380fb81670B76786c7d708a03811e82320B90bca5cfe5cf0A85930F> DC 76 /L <00822c017fbf800081f1829402806382810Bcc7cd56dc12203802c80670B6d3a602e 192c0A7b6d0781f50381f180bb096b04819f80378177802180e880210B2080147c30e203 810d822d0B91c1a0d4e4d40A8693077ef00A7c6d0F> DC 77 /M <008341017fcf800083708294027fd580130A7a6d0780d50A85920B688149813c9a0B 749883cc8ae60380df82200381248000098e03829d821f03822b80760B6c3763221a1a0A7b 700781080A85930B38862f9642de038306822d0B90bea5d4e5d40A8593077f4b03817180a1 03812f8294077f4e0A7a6d0Bc979d36abe2203803980670B6d3c5f301c2c0F> DC 78 /N <00829b017fc27ff282d582940281018294077f700A7a6d0B9381a981b6720B936b9c 59943e03803880670B6b35582d0f2c0A7c6d0780ef0A84930B27821b8c34e50380d5820203 81b27ff20999038266822d0B92c2a9d1ebd40A8593077f1e0A7b6d0Bd07bdd6dc71c0381ce 80aa03810182940F> DC 79 /O <0082d201801d7ff182b482a1028248828104820182ab81a082ab815482900480f9 827080aa8229807481dc048017815a7fe68073808c80120480d67fe7813c7fe9818b800504 81df802382238063825680ab0482b6813282f382188248828102820e827104828e821a822c 810481ed809f0481c7806381928029814c80150B597529750489048040806e80a3818580e3 81ec04810b822b81438267818d827d0481b6828981e98289820e82710F> DC 80 /P <008263017fd48000826882940281908294077eeb0A7b6d0Bca7ad96cc522038044 80670B6d395a31162c0A7b6d0781260A85930B5082148226c50380e081300B81848389888b 0480fc81418151813b8171813d0481ca8142822e8162825881b804827581f3826a823e8237 826a048209829281ca82948190829402812882400B8fb8a2baddb70481d6827482008239 81f581e90481e6817d818d815b812c81590B6c803b78459903812882400F> DC 81 /Q <0082d201801b7f4882b082a2028207826f04827d821b822a812181f480bd0481d0 8079819d803481518019048124800980ec800b80c5802b048058808380a2816b80d881cf04 80fd82138134825c817f82790481aa828981e0828a8207826f0280b57fc00B918eb0b3c9b6 0B8e819c7faa800Ba283c48ae497048245805783058179828d823a048253829781dc82b2 8176829b0480fc827f808a8210805181a4048000810a8008803180c97ffd03801c7f5e0A8d 6f04807e7f84809f7f8580ff7f670481bc7f2d81f97f3f827f7fd20A708d04822c7f9781fd 7f7a819a7f980481467fb2810e7fc380b57fc00F> DC 82 /R <008263017fcc8000823f82940281818294077ef40A7b6d0Bc879cd69ba22038033 80670B6d3a62311f2c0A7b6d0781080A86910B27822ea143ed0380d481470B9b7db67cd27d 03819b80000780940A85920B6c8258854b960B6f9562b859d103818a814e0481e38164823f 819f823f820504823f827581de82948181829402811482360B889e8fbab2be0Ba984df7ff7 590481e9820a81c6819e8181817a04815081618112815e80dc816603811482360F> DC 83 /S <0081f4017ff27ff081ef82a10281f0829e096c0B685840711e7a0480c082c9801f 8232808c81910480bd81498111811b813a80cd0481578098814a8055811d802d0480eb8000 809980058065802d048036805280258094802480ce096c037ff37ff40990048019802e805e 800080907ff704816e7fca820580948173813c048144817180f081ab80d581ec0480c38219 80cc825080f4826d048121828c8166828a818f82660481b7824381be820e81c281dc099003 81f0829e0F> DC 84 /T <00822c01802b80008266829402805481f404806882318090826580d3826e0B9984b8 87d1830B8e7d8d6e8a630380af807f048098802a80898016802f80130A7c6d07813b0A8593 0B18810f8e2af0038196825a0B889ea498bf97048233826c82368242823681f10993038267 8294077e0103803e81f60A967e0F> DC 85 /U <0082d201804c7fef830a82940281888294077ede0A7b6e0Bcb7be173cc2403805e 810104805080cc804480968059806104807a800d80d77ff181297ff00481db7fef821c804b 824580e703828f81fb0482a4824a82a98284830782820A8492077f1a0A7b6e0B997fc480cc 620B8b5d7d35751303821f810104820e80c381fe808081ce805204819e8024815780168117 8022048096803b80ac80b180c7811003810f821e0B94cca4e2f4e40A85920F> DC 86 /V <00826301803d7ff282c282940280e27ff2099503824c82210B9cb0b6dbf1e10A8692 077f370A7b6e0Be37ec0519c1303812a80880380ef82260B75c492ded6dd0A8491077ef80A 7c6e0Bc181cb5cd3230380e27ff20F> DC 87 /W <00834101803a7ff28398829402803b82830Bcb79ce6dd5220380c37ff209940381c8 81c90381ee7ff209990383198203048338824083508273839682830A8291077f400A7a6f0B d279d269aa1903823a80ab038220821a0B7ac885e4cfe90A8591077f030A7c6f0B967fb77f c4690B8e678c398e1c03810980a00380ee82260B7ac494ded6dd0A8491077ef60A7d6f 0F> DC 88 /X <008263017fa8800082b482940281748294077ee80A7b6f0Be079d861f60d038105 8146038028805b0B5d5b393a06340A7b710780f20A858f0B6a8141803b9d0B7a9c9bc1add4 0381138113038143806b0B9534842638260A7c6f07811d0A85910B2585249c0eef038169 816403822f822c04825382518277827f82ae82830A8691077f230A7a6e0B9480b785be6b0B 87656443533203815b819503813182270B6ac975dbbeda0A85930F> DC 89 /Y <00822c0180188000829282940281338294077eeb0A7b6e0Bd878dc57f8060380dc 811f0380a9805e0B6d3b593816330A7a6f07811c0A86910B3f831b7d30ca038142812703 8210821e0Ba2a9c5dcfde20A8694077f270A7b6d0Be07dd759a11803813381520380ec822e 0B6ac580cfc0d40A87920F> DC 90 /Z <00822c017fe38000823782940282378294077e5303805881f40995048097825780cb 82708134827009f8037fe4800d0A7f730781d00381ec80b5096b0481a880498171802580fc 8026077f71038237828b08890F> DC 91 /flat <008103017ff4804580a382450280138061048014808a800b80da802381010B8b 92a3a3b6940B9c6b934185260B6f5d5042352602800280460A90820Ba1a2c4c3e6e40B9595 abaeabce0B81a463c43ec00B617d4a67355203801e8245095703800280460F> DC 92 /natural <0081030180027f9680928215028003802e0Af7a7067f4209980681e70A095c06 80bc0968067e1802801b80730680a90Adf9e067f590A21600F> DC 93 /sharp <008103017ff27fa380a7820d0280127fa409970680990Ac7a2067f6a099706 80a00Aa18f08c80A5f700680860Aa18f08c70A5f710680900969067f640A39600680970969 067f5f0A617008390A9f8f067f7b0A617108380A9f90067f7102802980840680860Ac7a106 7f7b0A395e0F> DC 94 /slurbelow <0083e8018033806283b4815102803381510480a380ab812e806381fa806304 82c18063834780b183b58151095c04836b811f834180f3830980d30482b780a482558091 81f780910481948090812c80a580d580d80480a180f7807a812180558151095e0F> DC 95 /slurabove <0083e8018033808d83b4817b028033808d09a204807a80bd80a180e780d58107 04812c813a8194814e81f7814e048255814d82b7813b8309810c04834080ec836b80bf8391 808d09a4048346812f82c3817b81fa817b04812f817b80a381338033808d0F> DC 96 /lscript <0081f40180207ff781c182bc02807580fb04806d809d8077800780ee7ff904 81427fee8163803b8177807d0A63890B7257560a1d160480aa802c80d3810980d8813704 812b8170817581b281a6820b0481c2823f81d4828e819482b204815182d68111829e80ec 826a0480a8820b80888198807981270B6169435227380A946a0B9592aaa2c1b20280dd8161 0480ec81bf80fa822a813482780B959ebeb9de970481bb8264818c821a817381f404814b 81b98116818b80dd81610F> DC 97 /a <0081f40180147ff781c981c002813e81a30481a4817680e4800880878035048033 805d80c381d9813e81a302817b81b70A755b0B76a74ab126ad04809e81b0804181288022 80bc04800d807180057fe7807b7ff90480d1800681078060813280a3048127807f80f8800d 812c7ffb0481677fe681ad804081ca80690A708d0B4d3a1310388d0381c881b70933 0F> DC 98 /b <0081f40180197ff781dd82b00280b58164038107829d0B848e7f9670930480c782a6 80998298806882940A7c6f0Bc181c675b73703801d80470B7553a43ec9370481017fdc819c 804e81ce80dd04821681a9814e821c80b5816402809880ed0480df81f281df81aa816680a6 048140805880f78002809680120B56884f9f59c303809880ed0F> DC 99 /c <0081bc01801e7ff681a881c002818480660A7091048144804780f5800580ad802c04 807f80458075807e807880ad04807d80f7809d814080d281740B9e9ec4b4f0b40B887fa07e a1720B816f62656a440B8c52da60dc970481ac81d3811d81c580e881b00480948191804a 8143802c80ee04801380a880178044805880140480be7fc8813c8016818480660F> DC 100 /d <0081f40180107ff4820782b20281738073038206829e0B84907c966d930481c582a7 81998299816982960A7c6f0Bc281c272b33703817281a50B6aa12f9d0f930480988199803c 8123801e80be048007807180087ff680757ff70480d37ff8810d80578139809d04812c8076 8100801481337ffb0481737fda81bc803981db80650A718e0B706b4f3832380B5b7f70b675 c802814581a40481a3817980ee7ff58087802d048026806280d181d6814581a40F> DC 101 /e <0081bc01801b7ff781aa81c102807f80e0048091811b80ac815280da817d0B9997e2 c7fc970B94596d2050090480f780f680ba80e9807f80e002817a8072048148804380fa8010 80b1802a04806e804280748091807b80ca04823580fb81cd822680d381a104808581778042 812f802780da04801280958017803b8058800e04808c7fec80d87ff2810f80080Bb095d7b7 f9de0A728c0F> DC 102 /f <008116017f9c7f27819e82b20280da81af0A98f10B87a592d4b1ee0B8a889a90a687 0B947163399c2f0Bcb73c7cf8de80B588f2884066d0480ad826580988202808581af092a0A 796209d703802a7fdd0480227fb280197f8480047f5d0B7d7a68595d660B778a859c85a70B 7f97649f519a0B4e73641aaf240480247f3180457f72805b7fa704808380078098806f80ad 80d50380d4819109eb0A859e09160F> DC 103 /g <0081f4017ffb7f2681f681c40281f6817908ab0B5b80367a138a04815381c78114 81cb80db81b8048062818f801680f7809e80ac04806e807d8021804c807c802204803a8003 7fd77fc080057f6b0480407f0281477f1581847f8a04819b7fb781997ff081738012048148 803a8105804580cf80560B6c86479556b00B868c91979d9d048108809c815280a7818680dd 0481af810781c1814081b1817909c502809580190480cb8006810c7fff81397fda0B976d99 4b8f310B745d51492f410480b77f3c804b7f3c803b7f8f04802f7fd380627ffb8095801902 814a819f04817a8178815d811f814480f304812b80c580eb809b80be80c8048078810c80eb 81eb814a819f0F> DC 104 /h <0081f40180047ff481d582b202809580eb038111829e0B85907c966d930480ce82a6 80a18298807082960A7b6f0Bc381ca78b837038004800009d504807d808c80aa8105811b 81670B8b8ab4abc3950B906a7e3e7827038125806c048118803c81047fe681587ff6048196 800281ba804281d580750A728c0B736b502a322f0B65867dc181cd0381af81380481c18175 81cf81d3816c81b6048113819c80c78135809580eb0F> DC 105 /i <0081160180287ff6810a82910280f8806a0A708f0B706949352a370B61826eb174c2 0380e181a30B8288899f789d0B6b7d4a7432700B677d4e7935760A7c700Bb37eca79ba3e03 8038807c04802d805680127fff80517ff80480997fef80d1803880f8806a0280fa82820B52 ac09683a3b0Baf54f697c6c50F> DC 106 /j <008116017fa27f2a810d829102804981a90A7c6e0Bc77cc873ba2f038052805f04 8041800b80327fb580147f640B7b736d585b610B71867a9b7aa60B80956fa35aa20B457c5d 12b31e0480637f3a80877ffc809a80510380e381aa0B838a829774960B687e4f7637720B69 7c52793b770280fe82820B51ac09683a3b0Baf54f697c6c50F> DC 107 /k <0081bc0180027ff681da82b302809780ee03811282980B8592849e6e9b0480d282ac 80a7829d807682980A7b6f0Bb17fc883b746038002800009d403808b80b90Aaea50380e3 80590B88639441a72a0B8e71a971bb770Ba98cd5c2ede60A72900B5044301d11770380f9 81120Aead80Ba19cc7b7f3b70A8591077f460A7a710B907fb07fa7660B796c6458544c03 809780ee0F> DC 108 /l <0081160180297ff9812382b70280f1806a0A708e0B706c4632293e0B69897ab57ec5 03811f829b0B838c899e759c0B697d51773a740B657c4a782f750A7e6f0Baf7ecc79bd4003 803f8091048035806c800d8006804d7ffb04808c7fee80d0803c80f1806a0F> DC 109 /m <0082d20180037ff582b381be02803781a60A7c6f0Bcf7bbd5fa815038004800009d1 048084809180a9811c812c81790Bc7b2a5419d240380f6800009d204816a807d819680f4 81f081540Ba5a8ead4d277038205806e0B755a60109b0904825c7fee8298803c82b3806b0A 738e0B6d6a59433b3a0B67796f9972a6038290813804829c816582b481b9826c81bd048217 81c381c8814f819a81120481a7814681d581bd817781bd04812581be80ca813d809d810103 80d181a30B8590829e6e9a04808f81b4806a81aa803781a60F> DC 110 /n <0081f40180087ff481d581bd0280a080f80380d881a20B889b829f679704809381ac 806581a7803981a20A7c6f0Bcc7ec56daf25038009800009d3048082808b80ac8105811e 81670Bd5c9ca78ba3c038126806c048119803c81057fe681597ff60Bbd8be1ccfdfe0A708b 0B746b512c34310B65867ec181cd0381b181380481c0816e81d381c3817d81bb04812c81b5 80cf813680a080f80F> DC 111 /o <0081f40180177ff581dd81c10281b0819804814c81f680b181a78066814f048020 80fe7fe98061805180130480b97fc6814c80148192806a0481d280b88207814581b0819802 814781a60481dd818781467ff280ae8013048019803380ae81c5814781a60F> DC 112 /p <0081f4017f957f2781e081bd0280a580e20480e081cb81d281d3817080c8048153 80778111800080ab80090B50844aa155ca0380a580e20280487f7b038069800204809b7fe5 80de7fef81108003048180803381d680b181e0812a0481ed81db813581e880c381610480f1 81f180e681af803881a20A7b6e0Bba7fcb7dba3d037ff77f810B72475b3b23380A7b6f07 80f80A85910B4580268036c20F> DC 113 /q <0081f40180127f2881ef81be02815e81a00481d0816381017ff4808f802e04801f 806680dd81e2815e81a00281a281b40A735404815c82208027816d8013808004800c8021 80427fe280a17ffc0480ec800f81258051814c80910381057f8b0B6c3861341a300A7d6e07 80fb0A81920B2d812c9043e00381ef81b409330F> DC 114 /r <0081850180188000818581bc02812281770B8d38f25de1a30B79a350a43796048105 819280ca813080ab80f90380db81a50B848d859a749704809d81b2806c81a7803a81a00A7d 6e0Bd67cc55bb315038019800009cf048082805f809d80bb80d181100B97a4b0cbd1e7 0F> DC 115 /s <0081850180057ff5817181c002817281bd09740B795e3c782a7d04807d81da8021 816d808b80f00480b480c08122806180cf80210B5d64256803850B609e56c651f0097403 80067ffb098e0B88a1d082e07f04810e7fde817e805f810a80e40480ec8108807f816280b5 81960B9998c796e3850Ba869b43ebd14098c03817281bd0F> DC 116 /t <0081160180247ffb812b822d0280fc822d09690480bd81ef808981b4803d81a50A7c 6d09c503802c805c0B73517119b32004809b800280c9803880ea80660A71910B594c080429 7d0380cf819209d50A879e092c0Aa5fd0F> DC 117 /u <0081f40180207ff781d981c0028084809c0380cf81a30B859188a0709c0B6c7e5878 44750B657b4a7730740A7d700Bbf7cc475b02b03803580a804802880788001800180547ffb 0480c17ff18115808f814780dd0A611a048118804381057fe281617ffb0Bb58edec3f8f20A 728c0B49310f0c328e0381d081b7092f0481628136812a80bf80d0805e0B72723e3c295d0B 729485cb8be10F> DC 118 /v <0081bc0180137ff481b581bf0280937ff4038110807804814980b581ae812481b5 817a0B85c240de25b00B644eb646aa1c048174810780f7807f80c580520380b881080B8080 7f807f800480a081fb80b581bb801781a60A7d6e0B937daf7eba6a04806681548062811d 806b80ef03807f7ff409940F> DC 119 /w <00829b0180187ff5829581c202819381c2096f0380b380820A7df20480af810d80af 81b6809781c20B7983166b03680A7f700B947ea77db36a04805f81648061811c806280f803 806b7ff50992038152813a03817a7ff5099003821d80a604824980dc82b28154828f81a20B 6eaa2fa92c77048238814b82b8818b820380b60A3b2e03819381c20F> DC 120 /x <0081bc017fd47ff481bd81c002812181680A4e3c0380d181a50B7b96719f5a9a04 807f81b6805881a9802a81a30A7d6e0Bb789dc88ec4a0380b280d10A290a0B6f695c584064 0B658b43923b6b0B77589d49bc500Bad89c9afe3d20Ac6e00480c2808e80d2802e80e28010 0B89709967ac6504814c7ff18182803d81a0806b0A728f0B49301f1005820380f781000Abc d40B8f94a2b2bfa70B9877bc6dc98e0B8fa961bb40b30B58763d4b262c0F> DC 121 /y <0081bc017fc77f2981a481c302812580ac0A48280380d080e30480c9810880ad81ac 809381c204808e81c7802581ae801081ac0A7d6f0B977daf7bbe680480638164806d8123 807680fc0380ad7ffa0A3e280B6d67523d2d4a0B6b8854963e840B686c6e4c8a3f048032 7f0880967fa680ba7fd70480f080218190810781a181640B859a88ba74cf0B709350953c86 0B6d726f557f450B8c73a06ea45c04817e812c813c80d0812580ac0F> DC 122 /z <008185017fe27ff4819481bf028048804603818a81a20B8788939d7f9d0B6e815d60 2d640480af81af806681fb8034815a0A90770B98aaaeb5dfaa0480e2816d80ed8168812f 8171037ff2801a0B7b7b707171690B81798a7591770B9d8693a6df97048089800580e17fe8 81167ffa0Baf90bccdcaf70A6f8904811c7ffe80c88061804880460F> DC 123 /dotlessi <0081160180287ff680f781bf0280f8806a0A708f0B706949352a370B6182 6eb174c20380e181a30B8288899f789d0B6b7d4a7432700B677d4e7935760A7c700Bb37eca 79ba3e038038807c04802d805680127fff80517ff80480997fef80d1803880f8806a 0F> DC 124 /dotlessj <008116017fa27f2a80e481c002804981a90A7c6e0Bc77cc873ba2f038052805f 048041800b80327fb580147f640B7b736d585b610B71867a9b7aa60B80956fa35aa20B457c 5d12b31e0480637f3a80877ffc809a80510380e381aa0B838a829774960B687e4f7637720B 697c52793b770F> DC 125 /weierstrass <0083e80180bd7f6882e181db02811680760480ee804580bc800c80be 7fca0B814fa122d41f0Bbf7de9b2efec048188801881688066815780a704818d80e28215 8182826781770482bd816d828680df827280b4048258807c82368043820280200B68703163 2b8e0B7c9e99acacbc0B928f9caf81bb04818e80c9816f802781b380000482197fc8829f 806e82c380bd0482db80f282ef813482d8816c0B71a44fb829b904821f81a5819081048151 80bd04813d8101814d8148817f817c0B9291a5a2bab00B8d8a9b91a79c0B8585848e7e9204 81c481e781508177813f8162048106811a80f480cc8116807602811e806004812c80338142 800681467fd70B8455681835310B529752d264fb0B8ea3a8bfbfdd0F> DC 126 /vector <008341018000815d834182a102800081e30782d403820781910A964d038341 81da08cb03821d82a10A6a4d0382d4821c077d2c08470F> DC 127 /tie <008025018012821b817482b4028175821b04815f827b812d82b480c482b404 805b82b48028827b8013821b09b80B90c0b8d3f8d40Bc280e86ef92c09b90F> DC 160 /Gamma <00825b017fbf80008298829402827e81e70382988294077dde0A7b6c0Bd17fdf 6bca1c038043806f0B6930522702250A7a6c0781400A85940B3a831a8d30db038130822a0B 8fb89ec3dac309e8048249826d82648236826a81e709940F> DC 161 /Delta <008264017fb9800081f6829f0281f7800003819f82a00969037fb9800007823e 02800c802d03814781f8038182802d077e8a0F> DC 162 /Theta <0082e50180187ff282cc82a30282a2824904823782da814c82a880d1824904 807e8209804781ae802b814a04801380f7800d80968043804c048072800b80c57ff28113 7ff30481707ff381cb80138214804c048267808c829d80e682ba814a0482d2819d82d88200 82a2824902824f822304828081a1822e80d481d780720481a5803b81688016811d801604 80d9801680ac80318096807204806680f680b581c0810f8223048140825a817e827f81c9 827f04820f827f82378264824f822302815581740B477f368842c309670380c580e8099804 80f781308117812b815c812b0B9580dc87f1750B8f7388598548099803822381b709680B78 6b70545c480481c6816b81748174815581740F> DC 163 /Lambda <0082ae017fb28000825182a3028208808a0381c382a3096703802880770B64 574623101d0A7b6c0780be0A86940B27873ca768e703816981f704817281b881a4807e819e 80440B7f777c6e78660B706a4a6c326a0A7b6c0781090A85940B6e825b8650960B70976ac5 67e00F> DC 164 /Xi <008285017fdb800082aa829402827781df0382aa8294077dec03806481df09960B 95beaed6f0d60781380Bc57fcb6abf2a099602812081780B49802e8038bf096a03808680e1 09960480b9812c80e081258129812404813c81248194812a81aa81190B91738b5a88480996 03820381b7096a0B786b6f555a4b0481a1816e814181788120817802806580600B3d803398 3fd6096a037fdc800007821803822880b609690B6b43522a102a077ec40F> DC 165 /Pi <008300017fbc80008349829402834382800A8694077d2b0A7a6c0Bc77bde72c928 03803b806d0B6b34512c07270A7a6c07812f0A86940B3985218e36d903811e8216048139 8275816d827081c5826f0481e0826f823f82778257825d0B916d874e81390381e1806d0B6c 36502b06270A7b6c07812f0A86940B3784208c36d90382c982280B95cab1d3fad80F> DC 166 /Sigma <008250017fad80008277829402824581df0382778294077dfc0A7969038134 813f037fb6801c0A78640782140381f580b609680B6b46572a162a077eda03819381580A85 8f0380f2826f0780bc048210826f823e8241822d81df09980F> DC 167 /Upsilon1 <00826c018057800082db82d30280bd80610B71475f3422320A7b6d0780e5 0A85930B4781429750ca038152813a04817e8181822082848268829f0Ba38ea56f9d580B77 60924caf5b0482fb827882e282ef826d82c904823382b7820b828181e982520481ab81ff 817281aa813d815104813e81ba813e826d80e582b50480c682ce808682e6806582c30B5450 9d58c5390480ff823a80fc81a180fb813f0380bd80610F> DC 168 /Phi <0082fb01801b800082e1829402826a82800A8694077ed30A7b6c0Bca7bde77c928 048106821f807a81fb8037817f0480168142800d80f2804180bc048075808380c38077810d 80700B6b32512903240A7b6c07812d0A85940B3685228f38dc0481c58078821280868259 80b00482a480dd82df812882e181830482e381c382b581f7827c820e04824f822082208225 81f082280B95ccb0d4fad8028180820f03811480890B5685298c0fb004807980f380908143 80aa817f0480d081d8812482048180820f0281e9820f04823a8204827b81dd826f817f04 82658130824080dd81fc80b00481d5809781a9808e817c80890381e9820f0F> DC 169 /Psi <00831b01805580008376829902813e80ed0B5a832b8510a40480a4814380db81cc 80e981fe04810c828480dd82a5805d82950A79680Bd183be54ad170A6112048037810280a9 80d7813680d00A641d0B6c364f2b05270A7b6c07812f0A86940B3985228f37d90A9ce304 823a80d882be810882ea81a60A9fee0B92c29bece7e90A879804830082a582be8281829a 820a0482688166826f80fb81aa80ed03820282280B94c8b2d3fad80A8594077ed10A7a6c0B c77bdf73ca2803813e80ed0F> DC 170 /Omega <008300017fe4800082ee82a302820e805a09050A91bb04823680b282b88100 82e38198048317824f828282a381e082a304813282a3807b824a8048819804801e81068070 80b280f880950A6f4509050B3e7f329740d60969037fe5800007810f03812680b40480b6 80d180a0813080be81980480e3821b814a827e81d7827f0482638281828f8212826d819804 824c812381fd80cf818780b4038154800007810f03829480b0096a0B6b425229102a 0F> DC 171 /alpha <008254017ff77ff4822d81df0281918135048193817f818881d3812b81d704 80b681dc803e816c80118109047fe0809c7ff1800c807a7ff70480e77fe5812f80268169 80770B8358860db8020Bbb73ddb9ede50A6c8e0B6e6551412c540B5d945dc15ee40481b1 810281dc8161822d81a60A47b90481c581a881ac81788191813502817680f204815580a0 8118802380b78013048049800080488080805a80c904806f812280ac81a7811081bb04818a 81d48178813c817680f20F> DC 172 /beta <008204017fb47f1d81e682e602800b8087037fb47f1d09d9038047804b0B9559 b039dd2f0480e27fec81218002815280280481a2806681d280ce81bb81330B72bc3fd90aed 04818f81be81ca81e481e082370481f3827e81cc82d1818082e204812382f780d382b580a7 826804806981fd802a8108800b808702807d815004809381b480bf8287812582b90B9a8dbc 8dd2780B9f639b34930f04817981f2814b81a280f281b70B6a85438846670B8559bd6dd56d 048177818c816b8109815780c20481478085812f803f80f280220B63724170237d048057 803c80508088805d80c303807d81500F> DC 173 /gamma <0081ca017fe17f2181b581d60280a7804b0480ab809f80c181b4806181d204 801281eb7fef81657fe181300A9a7e0B8ea4abdfdac0048094814280898077808a802c04 80587ff480297fb4801c7f680B7c697c409a3b0480827f16809f7ff380a680220480ce804c 8216819b819881d30B4d953e523b2f04814b810e80f080a280a7804b0F> DC 174 /delta <0082100180007ff381c482e30281a582610B72ab60d23aec0B619534a0128d0B 596b4737560f0480dd8230811e81e8814481b10480b4820080148164800280d8047fe57ffc 80d67fa0817880530481cc80b181da813d81a481ae04817a82028122824c8108828c0480ed 82d3815282e981898261099c028075812d048095817680f381e08142818e04818781478157 80a28127805c048102802780ae7ff38075802c04803c8065805980ed8075812d0F> DC 175 /epsilon <0081b80180117ff7819981db02819281b30A879d04810981ee806381cf8028 813704800280d680088055806880180480a87fef81017ff2814a80010A88a00480b67fff 805c8046806f80e70780dd0A86a6077f240480a381aa80fe81c2819281b30F> DC 176 /zeta <0081cf01800b7f4e81ac82d30280dc8226048071824a805e82bc810082b60A82 960480ca82d4806c82e4805182a204803082558089822580c4821004805981a98005812b 800c80900480148007805e800480d180000Ba080c585e1720B9b6c8b42792d0480df7f46 80857fa9805c7f870B7174745f83540B9f69dc73fe7b04811c7f6581597f8e816d7fcf0B8b a787d962f1048107807080598028804780a10480308124808b81b280e482090481108205 81b881f581ac82430B7aa053a2399e048132825b8105824380dc82260F> DC 177 /eta <008207017ff77f1d81cc81d70280aa81160480b6814c80db81c0808c81d5048042 81e8801181897ff781530A97730B8995b9efd8d804807e818d80588112805280fe038008 800009d6048084807e80c5815d8143819d0481af81d2816c8127816381070380cf7f1d09da 0381af80fc0481bd813281ef81b4819f81d204813381fa80d6816580aa81160F> DC 178 /theta <0081ed01800c7ff481d782c002805581f2048018817c7fe0808d8045801e04 806c7ff480a77feb80dc8000048123801c815e8067818380a70481b7810081d5816781d8 81cf0481d9821581cf8270819682a104816b82c5813082c780ff82b10480b3828f807a8239 805581f202807e81540780e904815280fe8112801780a9800f0B537d3dae38d304805780b3 806b8106807e8154028171817b077f1704809b81c680da82a8813b82a60481b282a5817e 81bd8171817b0F> DC 179 /iota <0081180180007ff680d081cc0280c381cc092e0380128082048006805c7fea 800080297ff80480717fee80ac803c80d180700A718f0B6f69483128330B618270b575c503 80c381cc0F> DC 180 /kappa <0081fd017ff37ff481db81d902806d81cd037ff4800009d703808a80e70B8882 908398860380db804a0B914ea126e02b0Bb585ddabfed20A6e910B5a57282e0f7b0380ec 8121048114815081378185816981aa0B8854a933d84d0Bac9a9dd86ee104813081f180fe 8126809181050380c581cd09280F> DC 181 /lambda <0081c8017fbb7ff4819782e30280e281ce037fbb800009dd0380eb814803 80e980890480e8805480f37fe481437ff70481778002818b804a819780780A6b890B736765 4846460B477b45c846ed03811682140481188243813182ec80cf82e304809182dd80738289 805f82580A9d750B90a2bbd7e4b4048105826180fb81f580e281ce0F> DC 182 /mu <00823b017fb27f2181f381cc0280cc81cc092803800d805f047ff880137fe07fc9 7fc27f7f0B756761308a240Bb073b2b5b3d20480007fb8800b7ff9801e80370B8e4ea834df 410480d9800c810e8066813a80b1048130807c810f801681527ffa04819e7fd981d7803d 81f480730A67880B746a4818262f048167803c81848095818c80b00381da81cc092a04816c 81748154811b812980c9048111809b80d38034809c80270480428012808180c3808b80e803 80cc81cc0F> DC 183 /nu <0081c8017fef7ff781ab81d50280b681330480b7816a80c381c9807881d404802b 81df8001817d7fef81430A9d7e0B8896a6e4c7dc0B9b798c188b030380457ff809a503811b 80a804814f80dc81b1815581ab81a40B7da64fc22fa5048124819881928157810180bd0A23 1d0380b681330F> DC 184 /xi <0081e1017ffd7f4e81be82dc02811d82bb0A84980480eb82de80a382e8807d82b4 0B726d785483400B9164af55cb470480718202803a81a6809381500B526728490c1b048002 80bd7fef8075800780410480367fdc80e3800f81197ffc0Bb66c9e23680b0480b07f628071 7fa9804d7f820B76757b63865b0B9d6cc971e9750480fe7f5c81437f7d815e7fbd0B90a894 db74fc04811a807180838038804c806d0B669a6bc777e60B95b4c0d3f0ec0481ba80d281e2 81b580c5816404806481a1809c820580f1822d048119821f81b881f781be823e0B83a44fac 36ae048144826f8115825c80e9824d0B1fac3efcb4ee0F> DC 185 /pi <008263017ff27ff4824781e802801380910A6d7f047ff580627fde7ff0802f7ff5 0Baf83d0b4e2db0480b880a480d7812380ee8181038172817f03813c80a304813080728115 801f814e7ffe0B9f6ecd79ea8a0Bab9ac3ccd9f80A698b0B6d62400a141a0B5b8e77d67dee 0381c6817e048218817f822e8191824881e00A68880B796f70655d600B657a467d2a7e03 80db81c904806c81cb804181bf8022814d099f048054818c8097818180cd81810480bb8136 80938084805a80550B71745a6e4a7a0B6b8e6eac6fc20F> DC 186 /rho <008219017f9b7f1d81d981d8028094813b0B8daca1dcccf20Ba091cc93ec8404 8199818b8185811d817580db04814e803480e27fcb80498046038094813b027ff47f1d03 803b801604807b7ff980c67fe6810c7ffa04818d801c81e680ae81d881310481ca81b08163 81e480ed81d604805d81c680458158802280e3037f9c7f1d09d80F> DC 187 /sigma <00820e017ff97ff6821981f0028085814b0B98adb6d4e6e80Ba690cf80e76004 8186814d815580ac812c80670480b77fa67ffd804b8085814b02818481990481d1818e821b 8184821a81eb0A6c850B7b71716761620481c181c8815e81d6813481d70480ea81db80a1 81c98069819704801f81567fed80ee7ffd808a0480187fe380e17fd28152803204818b8063 81b780aa81be80f60481c3813981ad8168818481990F> DC 188 /tau <0081a7017ff67ff6818f81e802817e81e90B776d6861535e04811d81c080df81c7 80ab81ca04804081d1800981c67ff7814f0A967e04802481928057818480958181038060 80bd04804f8081802d801180827ffa0480d97fe2810d8041812e80810A6b8c0B6d6148141c 1a048080802d80aa809980b080b20380e9818004814c817c81718179819081de0A6e8b 0F> DC 189 /upsilon <008206017ff17ff581c281d702800881460B8e9f9cbfb7d40B8d8aa795b080 04808c8156801e80ad803d804d0B8d55b333e02b0480e87feb812980148157804c04818f 809081b380e981bf81400481c4816781ca81b181a781cd0B689245883b6b048154818e8180 814b8184811c04818f809b80f57fd9809d802504804d806a80fa814080bb81b20B6ba737af 119a0B5366373225020A97780F> DC 190 /phi <00825d017ff37f238229829d0280f17ff30Baa87d18ef7a10481b5803a81f88077 821780c70482368115822c816e81e881a50481c281c4819381ce816481d5038194829d0959 03813481d70480f981d380c381c8808f81aa04804781818006813b7ff880e7047fde805f 802a800d80a77ff503806a7f2409d40380f17ff302812981b20380af8012048033802e803d 80a58066810704808c816180c781a2812981b20280f9801503815c81b20481cd819881dd 813a81b780d6048194807a8155803580f980150F> DC 191 /chi <0081db017fab7f1c81c181d70280a380ab037fac7f2a09df0380b480340480ba 7ff680c47f32810a7f1f0481597f0981787f9281847fc60A67880B745a601c2b280480da 7f8380d3802280cf80550381c181cc09230380c180d00480bc810a80b881bf807e81d40B65 8a487c356804800f8197800381617ff681310A98780B8ba3a8e9d9d80480988170809f80d7 80a380ab0F> DC /FontBBox {-107 -236 948 763} def end /Dutch801-Italic-DECmath_Italic bsd definefont pop %%EndFont %%BeginFont: Dutch801-Roman-DECmath_Symbol % Bitstream Fontware PSO Font -- Version 1.6 % DECmath Font Version 1.0, created 4-13-89 % % Copyright 1989 by Bitstream, Inc. All Rights Reserved. % Copyright 1989 Digital Equipment Corporation % % This product is the sole property of Bitstream Inc. and % contains its proprietary and confidential information % U.S Government Restricted Rights % This software product is provided with RESTRICTED RIGHTS. Use, % duplication or disclosure by the Government is subject to % restrictions as set forth in FAR 52.227-19(c)(2) (June, 1987) % when applicable or the applicable provisions of DOD FAR supplement % 252.227-7013 subdivision (b)(3)(ii) (May,1981) or subdivision % (c)(1)(ii) (May, 1987). Contractor/manufacturer is Bitstream Inc. % /215 First Street/Cambridge, MA 02142. % % This software is furnished under a license and may be used and copied % only in accordance with the terms of such license and with the % inclusion of the above copyright notices. This software or any other % copies thereof may not be provided or otherwise made available to any % other person. No title to and ownership of the software is hereby % transfered. % % The information in this software is subject to change without notice % and should not be construed as a commitment by Digital Equipment % Corporation. % % BITSTREAM, INC. AND DIGITAL EQUIPMENT CORPORATION DISCLAIM ALL % WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED % WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL % BITSTREAM, INC. AND DIGITAL EQUIPMENT CORPORATION BE LIABLE FOR ANY % SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER % RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF % CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN % CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. % /n_chars 128 def /DC { /bits exch def /name exch def /num exch def num 256 lt {Encoding num name put} if CharStrings name bits put } bind def /bsd 15 dict def bsd begin /FontType 3 def /FontName /Dutch801-Roman-DECmath_Symbol def /PaintType 0 def /UniqueID 440175 def /FontMatrix [.001 0 0 .001 0 0] def /FontInfo 12 dict def /CharStrings 1 n_chars add dict def CharStrings /.notdef <0F> put /Encoding 256 array def 0 1 255 {Encoding exch /.notdef put} for /temp 15 dict def temp begin /get-word { 0 s i get add 8 bitshift /i i 1 add def s i get add 32768 sub /i i 1 add def } bind def /get-byte { s i get 128 sub /i i 1 add def } bind def /get-name { /len s i get def /i i 1 add def s i len getinterval /i i len add def } bind def /eval-arr 16 array def eval-arr 16#00 {get-word 0} bind put eval-arr 16#01 {4 {get-word} repeat setcachedevice newpath} bind put eval-arr 16#02 {closepath 2 {get-word} repeat moveto} bind put eval-arr 16#03 {2 {get-word} repeat lineto} bind put eval-arr 16#04 {6 {get-word} repeat curveto} bind put eval-arr 16#05 {4 {get-word} repeat get-name do-char} bind put eval-arr 16#06 {0 get-word rlineto} bind put eval-arr 16#07 {get-word 0 rlineto} bind put eval-arr 16#08 {0 get-byte rlineto} bind put eval-arr 16#09 {get-byte 0 rlineto} bind put eval-arr 16#0A {2 {get-byte} repeat rlineto} bind put eval-arr 16#0B {6 {get-byte} repeat rcurveto} bind put eval-arr 16#0F {end PaintType 2 eq {temp begin stroke exit} {temp begin fill exit} ifelse } bind put /do-char-arr 16 array def do-char-arr 16#00 {get-word pop} bind put do-char-arr 16#01 {4 {get-word pop} repeat} bind put do-char-arr 16#02 {closepath 2 {get-word} repeat moveto} bind put do-char-arr 16#03 {2 {get-word} repeat lineto} bind put do-char-arr 16#04 {6 {get-word} repeat curveto} bind put do-char-arr 16#05 {4 {get-word} repeat get-name do-char} bind put do-char-arr 16#06 {0 get-word rlineto} bind put do-char-arr 16#07 {get-word 0 rlineto} bind put do-char-arr 16#08 {0 get-byte rlineto} bind put do-char-arr 16#09 {get-byte 0 rlineto} bind put do-char-arr 16#0A {2 {get-byte} repeat rlineto} bind put do-char-arr 16#0B {6 {get-byte} repeat rcurveto} bind put do-char-arr 16#0F {closepath exit} bind put /eval { /s exch def /i 0 def { /t s i get def /i i 1 add def eval-arr t get exec } loop } bind def /do-char { t s i matrix currentmatrix 2 {6 index} repeat translate 2 {8 index 256 div} repeat scale end CharStrings 5 index get temp begin /s exch def /i 0 def { /t s i get def /i i 1 add def do-char-arr t get exec } loop setmatrix [/i /s /t] {exch def} forall 5 {pop} repeat } bind def end /BuildChar { exch begin 0.2 setflat Encoding exch get CharStrings exch 2 copy known not { pop /space } if get temp begin eval end end } bind def FontInfo /version (Fontware-PSO 1.6) put FontInfo /OutlineResolution 1000 put FontInfo /Copyright (Copyright 1989 by Bitstream,Inc. and Digital Equipment Corp. All Rights Reserved.) put FontInfo /Notice (Dutch 801 is a registered trademark of Bitstream, Inc.) put FontInfo /Date (1989/4/13 12:16:50) put FontInfo /FullName (Dutch 801 Roman DECmath_Symbol (TM)) put FontInfo /FamilyName (Dutch 801) put FontInfo /Weight (Medium) put FontInfo /ItalicAngle 0.00 put FontInfo /isFixedPitch false put FontInfo /UnderlinePosition -100 put FontInfo /UnderlineThickness 60 put 32 /arrowleft <0083e801803e808c83a981d00283a9811308b8077d03038179819e0A6ab3 03803f81550834038163808d0A96b30380ac81130782fd0F> DC 33 /arrowright <0083e801803e808c83a981d002803f81130782fd03826f80c00A964d03 83a9810908cc03828581d10A6a4d03833c814b077d0308480F> DC 34 /arrowup <0081f40180577f53819b82bc0281167f540682fb03816881830Ab39503811f 82bd093403805781980Ab36b0380dd824f067d0509b90F> DC 35 /arrowdown <0081f40180577f53819b82bc02805880770380d47f5409cb03819b80770A 4d960381167fc10682fc0947067d0403808a808d0A4e6a0F> DC 36 /arrowboth <0083e801803e808d83a881d10283418149077d66038179819e0A6ab303 803f81550834038163808d0A96b30380a7811607829a03826f80c00A954d0383a9810908cc 03828481d10A6b4d03834181490F> DC 37 /arrownortheast <0083e80180377f4b83b082c40280377f740Aa85803835d8248038306817d0Ab4 6b0383b1828f0A4bb5038255824d0A954d03833582700380377f740F> DC 38 /arrowsoutheast <0083e80180377f4b83b082c3028037829c0383357fa003826a7ff60A6b4d03 837c7f4c0Ab5b503833a80a70A4c6b03835d7fc803805f82c40A58580F> DC 39 /similarequal <0083e80180aa80bf833d81c00280aa813204811a817f8160819581e5816904 827f813682b08126833e818208bf0482aa815a828b816e81e781a104816b81ca811681b4 80aa817108410280aa80bf07829408b7077d6c08490F> DC 40 /arrowdblleft <0083e8018027803183c081dc02812881710Aeabe0A65ae038028811808 5f03817780320A9bae0A16bd07829808b3077d100A20b70Ae0b80782f008b2077d68 0F> DC 41 /arrowdblright <0083e8018027803183c081dc0282c08171077d68084e0782f00Ae048 0A2049077d10084d0782980A16430A9b520383c080f708a103827181dd0A65520Aea42 0F> DC 42 /arrowdblup <0081f40180237f3b81cf82d302809081d3067d6909b20682ef0Ab8e00Ab7 20067d1109b30682970Abd160Aae9c03810a82d3095f03802481850Aae640Abeea0F> DC 43 /arrowdbldown <0081f40180237f3b81cf82d3028090803b0A42ea0A52650380e97f3c09 a10381cf808a0A529b0A4316068298094d067d110A49200A48e00682ef094e067d68 0F> DC 44 /arrowdblboth <0083e8018027805983c0820402812880c50781970A17430A9b510383c0 811e08a203827182050A65510Ae943077e690Aeabd0A65af0380288140085e03817780590A 9baf0A16bd0280d080f80A20b70Ae0b70782480Ae0490A2049077db80F> DC 45 /arrownorthwest <0083e80180377f4b83b082c40283b17f740380b3827003817e821a0A95b303 806c82c40A4b4b0380ae81680Ab49503808b82480383897f4c0Aa8a80F> DC 46 /arrowsouthwest <0083e80180377f4b83b082c30283b1829c0A58a803808b7fc80380e280920A4c 950380377f810Ab54b0381937fc30A6bb30380b37fa00383b1829c0F> DC 47 /proportional <0083e80180f1807082f681e302820781470481ea810b81c680af8179 80ac0B3b7d11bb11fb0B80c4affcf5fd0481be81a481e9817a8207814702822a80ee048257 8094828b805582f6808008a9048291809c826880ba823b8113048251814182678171828c 81940B9e9dc49eea9708a40482858202824b81cc821881690481f881a881cc81e7817d81e3 04811e81df80f1817f80f2812a0480f280d381298074818980710481d9806e820780b0822a 80ee0F> DC 48 /prime <00811601802c80aa80e9826902804780aa0380db81f70B91a79be267f10B448f 2b56242703802c80aa099b0F> DC 49 /infinity <00834101806b806b82d681ea0281a680ec0481cc80ae81f7806a8249806e04 82ab807282d680d682d6812c0482d58184829f81e7823e81eb0481eb81ee81be81a8819b 816804817781a7814b81ec80f981e904809781e4806c8181806c812a04806c80d380a3806f 8104806c0481558068818380ae81a680ec0281838145048167810c814580b880fc80b40B3f 7c15b715f30B80c1aff4f0f404813e819b81658175818381450281bf81110481db814a81fd 819d824681a20Bc184eb48eb0d0482b080b28215808181bf81110F> DC 50 /element <0083e80180aa8000833d826c02833e800008ba077e9b04813d803980f2808d 80e4812507825a08b3077da60480f781ea8144823281d9823307816508b9077e9b04811b 826c80aa81f480aa81360480aa8079811b800081d980000781650F> DC 51 /suchthat <0083e80180aa8000833d826c0280aa80000781650482cd8000833d8079833e 813604833d81f482cd826c820f826c077e9b08470781650482a5823282f081ea8304815807 7da6084d07825a0482f6808d82ab8039820f803a077e9b08460F> DC 52 /trianglelgup <0083e80180757fde837282e30280757fde0782fe0381f482e40380757fde02 80ba80080381f4828403832d8008077d8d0F> DC 53 /trianglelgdown <0083e80180757f2b8372823002807582310381f47f2c0383738231077d0202 80ba82060782730381f47f8b0380ba82060F> DC 54 /slashnegate <0080000180007f4b81a282c30280347f4c0381a382b10A4c930380007f5f0Ab4 6d0F> DC 55 /mapsto <008000018024808180b981dc02806181dc0944067ea509bc06809209d808b809 280680910F> DC 56 /universal <00827d017ffd8000828082ce027ffe82cf038108800009ec03828082cf09 160381ca81f7077ee503806282cf091c0280cd81a40780e003813e80670380cd81a4 0F> DC 57 /existential <00827f0180298000823282ce02823380000682cf077dff082707819f06 7f29077e80082c078180067f0f077e58082607820a0F> DC 58 /logicalnot <00834101807b80af82c581a402807c816b07820f067f4509ba0680f507 7db708460F> DC 59 /emptyset <0081f401801c7fae81d782fe02816782ff0A663204812482c380f682c580ca 82ba04806c82a1803c8244802a81eb048013817c801780f1803b80860B8d59a439bd190A59 1009aa0A9edb0480c67fed81027fef81347ffc048191801481ba807b81ca80d10481df8140 81e181d081b6823a0B70a659c43ce00Aa2e509530280a9803403815d8267048174822f8178 81f6817881b90481798155817d80ee816c808b0B7850671431060B52742b7f0ca3028141 828e038092806204807580e8807081ac808c82310B8ab1a0e6d6f30Ba489c482df6a 0F> DC 60 /Rfraktur <00831a01801d7ff582ee82f50282bc81ea0B8781a484ab8b0B8586828f7a90 0B70835e804f880B658e6bb46dcc0482af833281a48322817a825604814f8311807a8330 802c8284047fd281bb812b819b804281210A8b6b0480ac813b80f8818780a781ee048087 8216805882398052827004804c82b6809f82e880dd82cf04811882b78128826f8131823704 813d81e98140819a8142814c04814580e38155802380c5800f0B6b7d477e3a930B709a8bb3 94ca0B8ea36fcb49c70B487a4433570b0B9851cb39fd380480f17ff4812b80178152804a04 819480a2819e813c819a81a60Ad8950B9a68a74bac280482298117822180c98228807d04 822c804f8238800d82687ff80B9776a894b4a20Ad2d90A70900B6e6e554b37540B618b63bd 63d604827680f48287819f824c81d10Af09902828f81f703819881bf048191820381878251 81a882900B95a8bdcbedc504825b82cc82438275824a82470B865ea33ac5300F> DC 61 /Ifraktur <0082bb0180347ff4829382f502810081a60480ad81a2806a81e2806e823604 8071828480b882d6810b82b0048160828a818b821581f1821104824d820d8289825a8271 82b1096b0B87527c113f160481db824c818f82d3813582ee04803683387ff881858100818f 089702804980020B82a684d69df60B8e91a49dba960B9b79a85fb6490480fa802181268000 81677ff80481bb7fec82138004824980480482bb80d681ff814881f5819d0481ed81eb8280 81ed827d8152099504829881e48218821481d381c80481ae81a081b3815f81cd81320481ed 80fc822580cd8233808d048243804781f4801181b6800d048169800881488051811f808504 80c680f5802a80bc8035800209940F> DC 62 /latticetop <00830a018039800082d082ce02803a82cf084607812e067d6b09ba06829507 812e08ba077d6a0F> DC 63 /latticebot <00830a018039800082d082ce02803a800007829608ba077ed2068295094606 7d6b077ed208460F> DC 64 /aleph <00825a0180217ff1823782a1028022801c0A826804807c7ff580e0801280b7 80800480a680af807880d68082810c0B87a7a7c2c3db04810f8120815b80dc81a180900B9e 60bc3dca120B8572835b90510B857c8e8391870B94969abc9ada04822680b481a7811e8166 815e0381e381e60Bab619a3fae450B9588a4b0a6c40B85a96cc74ee00B6a914ca243be0B7e 877c9373920B6581594a58360B7e539d3ebc22038152817004811481a880d481e2809f8223 0B6c995ab450d30B7c8d7ea272ab0B6b905944573c04802981ff807681b880b1817a048059 812c802680f48045807a0B8c519e2c5d220F> DC 65 /Acursive <008276017f647f96820582ec02818e82c404817d824d811e819f80de813d0B57662e 4f023a0B9b7db57acf7904808980b980047feb7fb98006047f76801d7fd580a37fea80bd0A 6c7e047fa780887f3b7ffb7f717fad0B975ec369e07c0480277fe08095809780cb80ee04 80fa80eb812980e9815880ee04815080b181488073814580350B7f6a804c95400481887fd7 81f2806d820680860A7b940B746f4f31344d0481a2807b81ad80e081af81010B9f88b99ad2 ac0B667c4d7a33790481bc81c581d1825481fd82ed0B5b71376311570280f2812f048127 818a815881e88181824904817381e881688187815f81250B5b7e3783138a0F> DC 66 /Bcursive <008265017fe27fd6826482e9028066826c0A7f6d0Bbda9e1b7cd5d0480a281ec808c 81a28073815a04804e80ee801880887ff0801e0B786a6c50783a0Ba19ac3b4e5cf048072 8083809880de80bf813a048107813181718121818280cb0481908088816c803f8143800b04 80e2801380c4806f80d580c30A74770480a2806380a47fea81177fd604816f800f81de8070 81da80e60B7ebc58e823fe0481d181a7824481fc825f82690B88a48bd572f30B6e974e8c39 8004819e82a0812181ff80de81980480f481d3814c82b1813282d90B798a6b8662820480d8 82bc809c82958066826c0280c9814a0480f881a1812381e38169822c0B8c8cd2dbefcc0B95 778e548b430481d581eb81a481a38168816d0B73856589578b0A0a520F> DC 67 /Ccursive <008222017fee7fe4824c82da02819380db04817880a581518075812680490B6a6a3c 6c206f0B50852ea01ccc04803880ec8071816380a881bb0480d6820681328282819482900B a585ca70d34a0481f3822a81d081fa81b181d904818081a48141817f80fb816d0A8a6404 81578172819b81a481da81e1048209820f825a8261824b82ad0B7b9866a84eac0B67844c7d 347504814582a180d48233807d81c504803281667fe080e07ff080600B8648a716df0804 80eb7fc28179807781c680e40A4d770F> DC 68 /Dcursive <0082d2017fce7fcd82bf82db02802b817504804281ab807a8238809e82580480d4 8289814f82958194828e0B5e623a47152d0480eb81a480a28110806a80760B6c8547963385 04800480647fd47ffd7fcf7fd80B7c54fdc3fec40480a5800b81017fdd815c7ff60481d5 8016826080a08296810c0482d1817f82d28219827b827f0481f1832180f982d48073825704 8021820c801a81e9802b817502808f806d0480ea8121814281da81a582890482a0823b828d 810d81f6806e0481a4801880ed8053808f806d0F> DC 69 /Ecursive <008217017fef7fe5821982d602817780d50B725a5e3747150480fc8043805c802e 8057809e04805280f080ab813b80f381510Ba089be85de800B9e97bcacdbc10481688191 80f381ad80f182020B7faba7e9d0fa048191829e81ff8252818d82010A90780481c58215 82218259821982940B7ab432cb06c004815882c480b48233809781f304807781a980a58180 80e6816604809281458040810f800d80c3047fe580847fe2802e80247fff04804c7fe38083 7fdf80b17fef04811e80138175807681a780db0A507a0F> DC 70 /Fcursive <00822e0180237fe0825c82db028061820609ac0B85a890f2bffd04811f82958176 825c81c882530B686c505f325504816981e9815881ab8145816d048117817180ea817b80bd 81860B616a41561f430480a3813c80ea81348132813104811880de80fd808b80d4803e0B5c 7835852aac0B76a38ac69ce30A6f7904805f809c802b805e802480210B7b56973fc04004 80a07fe280f08023811980490481498077816780f0817c812b0Ba095c1a9e2bd0B677f4f7f 36810481ad81b981cc820681f182510Ba492c8a5ecb704820e8297814e82e4811782db0B55 7828460f270B625a4d303b040F> DC 71 /Gcursive <008253017ff57f28823a82dd0281a981c60481db81ef823d825b823a829c048237 82e081eb82e481ba82d304814e82ad80d4823f808e81e8048043818c7ff681047ff5808804 7ff5803580197fe680747fdc04805d7fa180587f6180767f290480b67f4380ea7f6f8119 7fa20481597fe8817b8034819b808d0481c7810881c38109820e816a0481d2816c81968172 815b817b0A264504812c813f8155813c8180813704815a80e28123807d80df803e0B4b6c18 8703bc048025811480c48223814682740481d282cd82178243818e81c6099b0280857fdb04 80e7800081258061815b80b60A847d0B76696a535f3d0B726269435e240481047fd580e5 7f8e80ab7f670B5d9d51c75af40F> DC 72 /Hcursive <0082d2017f2b7fc582d382d1027f2c800e0Aee38047fe37fe8806d801b809a806404 80c680ab80ce80ea80e98132048133812b817f812681ca81290481a880de816d80488181 7ff904819c7f8b822f8049824780690A79960B7874452a324d0481da807e820b80f7821e 81260Aedbb0B627e447d257e0B899795ad9fc5048279820782a0826c82d482cb0B57712c66 025b048227823d820181d081dd8163048193816a8149817080ff817504811581ab818282a3 816582c90B729159824a7a0480f982a680c28287808f8264086e0B9187c4a6d2940480f3 824f80bc81b180ae818c0A16390Acf7704806b80d9804c80698001801a0B7371646b4f6a04 7f9980037f6280087f2c800e0F> DC 73 /Icursive <0081af017fd47fa481cc82d1028068820f0B9187a08fb0980B8a9e95bba7d40Bab8d ca8df68a0480c281e380b8809680367ff30480018018801a8090803380bf0A4d5a047fe5 80587fb37fe47ff07fa50480607fc680c4805b80ef80c004810d8108812481538139819e04 814d81e5815f822e817f82710B92a6afc2cedd04819482ce813682df810582c50B576b324b 14280B69655c434f220F> DC 74 /Jcursive <0081db017fcb7f29820582cf02820682c504819582bf816082f480ff82a40480aa 825e805a81ea805181790B7d558d2fb71f0Ba8a3cdc8eff00B5f6b378130a604809981f9 80c6824680f2827e04811c828881478287817282810480fe819f80c87fff802e7f6a047ff1 7f99802b8044805080770A6276047ffc80247fbe7fbf7fcd7f5e0B836d8d589e4e0B8e78a6 89b28f0480687f6180ae7f9d80d97fe6048117804f814180ea8165815f04818181b881a4 824181d682900B8d949fa5b0b50F> DC 75 /Kcursive <0082a4017fda7fc482b182d802807c807a04809a80ba80b480fa80cb813d0B94749d 5ea6490480ca80d780a380a9807c807a027fdb7fc40Ba599cbb3f1ca04807d806180bb80aa 80fc80f004811080bd81577fdf81817fd50481a77fca81ff803d821680600A7b950B716c53 40344e0481958058815581088143813f0481bb81908275821a82a782a50B868f93a97fb20B 75862e3f24360481e7822d818f81c3813881590B5d74396c14690480f381ac81278232813e 829d0B838e859e7eac0B788c6c8b60850480dc82ae80a28283806982580A866d0B938ecdb5 cb820480b9820c808581848074815104804680ca801880447fdb7fc40F> DC 76 /Lcursive <00825a017f8a7fab825682dd0281a081d20481d981fa8255825f825782ac0B81b63d b517ac0481aa82c8816a82a181328279048100825680de822e80c481f704808d81848070 81068040809004800180787fc7804e7fa380150B79755f536a450B8a73a783b187047ff7 7ffb801f80238049804e048093802480d57fbd81237fac0481877fda81d8802e8211808c0A 4b760481c6804e81a8801f81797ffe04810e801480db8084808480950480dc811c80e1815a 811e81ed0481358224814b825f8175828a0481e282b482298251818e81da0A92780F> DC 77 /Mcursive <008380017f357f7b833082dc0280bb82760B948bdbb3e88b048145821b80328057 7feb80150B6d6d535a365c0B6f82648c619b047f7a80427fa7807a7fc380a20A6c7d047f7b 80657f34800e7f367fbc0B815e9640ba3f047fab7f7b7fda7fb97ff97fe3048069807a80e8 816d812d822004812b819d8126811b81218098048121808281137ffe812e7ff40B9777b2a1 bbae0481b3808081f180e98231814e0482548186827781c0829981f90482798174826280ed 824d8066048248804782347ffd824d7fe00B8a739a72a87a0482ac7ff782e3803b830b806a 0A79930B74714b38345104829d806e82f6820382ff822e048308825983138284832282ad0B 858c919f8dac0B7e847b8477820482fd82c282d282ac82a782960482a382158236817d81f4 81160481e580ff81ac809f819580880B7b7c747b718104817c809881968271819082ac0B7e 9279a865ac04814b82e280de829b80be82890A7d6d0F> DC 78 /Ncursive <0082d2017f797f7782c482d902806082540A846a048081825980cb829180f082650B 926c904e8b360480e981b780968115806980bc048050808b801a801e7fe380030B777c6677 5e810B74927eae84bf0B8eaaabcbc9ea0A6277047fc2806d7f9280337f807fec0B79636e17 9a0d0Bae74eedefef604807c808380e981708117821e048155815e817e809181967fc90A88 810481e6803c822780b3825d812e048281818082dc825e82c082b904829c832482058260 81f382470A8a6f0B9197a4afc1b80B9f88b873c0570482a081d1821780cf81df80670481c5 811e818d8243813382da0480e382bd80a1828b806082540F> DC 79 /Ocursive <00829f017ffc7fe082a482da02813b829b0480aa8240802381a6800380fa047ff6 80ad7ff48050802f801504805c7fe980a37fd780e07fe50481c2801882d4814f829d824304 828182bf820b82fc819782c904816b827b8127823a80f181f20A99810B9aa5b6cadde304 8191827281cf827d81f9825b04828681ec820780c0819b8066048135801080868033806e 80c204804f817680c1822e814b82980A70830F> DC 80 /Pcursive <008251017fee7fb9825482d40280b280f70480e08168812e821d819682600Ba297c7 96cf670481fa81d381968103811580ed0B5e7b3d7f1d8a02806a82410B8d8bcbb3d49104 80cc821c80788151806581200B6b71566340560B8c749969a85e04803880a57fe37ff27ff0 7fc80B866f9c70aa740480537fce80937ffd80c4801c0A819604802a7fc580838077809e 80bf04818480a9827f81b0825082910482258360812c8213810d81e10A7b830481188214 814d829c813f82ca0B7d87758b6e8a04811582cf80838269806c825a0A7e670F> DC 81 /Qcursive <0082a4017fd37fa7828782d502821b80450481b67fc281467ff380be802a048128 805e8191809581e880e704823d8139828381a38287821c04828d82cb820582f9817682b504 80f08274806181ed803e8156048031811e803080d8805b80ab0480b5804d815080d28186 811b096404814180e080d680b980b1810e048081818180da8259815982830481d482ab821c 824e821181d70482028121814d806a80a0803a0B5b8d379d11a60A22210Ba96bc568f07404 809a7fd081177f91817b7fae0481c07fc3820e800b823a80440A61810F> DC 82 /Rcursive <008296017ff77fc9827882db02807482440B918cb3a9c8950B8e728c5b8a490480b5 81b2806880f6803f808904803680727ff57fdc7ff87fcc0B817e847d867e0B8482f2ddfee6 048095808780b380dd80d581320480f480fb811280c3812d808b048138807481717fed818d 7fdc0B8c79977ba2820481d27ff6820f8042822a80610A79970B6e6b514230520481a7805e 815481168142813e0481c881698229819d82608224048271824c828f82b3825f82d404820e 830a813481e7811081b40A7e840481878338815f82f28072825b0A82690280dd813a04810f 81968166821a81b9825b0B9590bba8c681048210821681c981ac8199817d0B5e6041601565 0B65734a652f580F> DC 83 /Scursive <00820b017fe07fdf821a82d60281aa81d70481c681f082178254821b82760B81867b 8f78940B6ea74cc321ca04810382f37fe781b680b181400480f0811c815b8105815480a90B 7b416131232404807380307fdf8083807080fa0A5c7d04802180c17fed80777fe180320B7a 64bd3cd0360480ef7fa7822380f88161816a048126818d80b381a880b582000B80c2a0dad9 eb048184828e820c8246819081da0A9a7d0F> DC 84 /Tcursive <00828a0180357fdb82ce82d9028035825b0A8d78048077827a8094827d80d4827004 811682628157824d819982420480ea81db7fe981208087803d0B9562cc19fd1f0Bac86d9a8 f9c20481c2805581f9809a822680e50A4f7a0481d4809d81a98062817180300481118041 80cc809580ca80f60480c78192814181f081b8823c048229822c82a5825c82cf82ce0A768b 04828082cb823f82ac8201828c0481958292813382c880ca82d904809b82aa806982848035 825b0F> DC 85 /Ucursive <0082bb0180077fe2829b82de02806982600A856d0B9c90d4b3d4780480c181f3802e 8082800e801b0B755e793da74c0480ae800e813b80bf8180812c0A847e04816b80e18146 8048815a80000481787f96823080658238806e0A79920B6b692e2d1d6a0481af80d68226 81cb8251822c04825d824682a282cd829b82dc0B7b880c5804540481d681ea817480f980c4 80750B2b414cb25bda0480c1812b8147826b814882b10B80907ca36ba90B798273816e7e04 80f282c28095827e806982600F> DC 86 /Vcursive <0082390180387fd8825e82da02803982460Bae9ce2afe9660480a981e3808f815d 8084811904807a80dc8070809e806480610B7c6e785c76490B7c5aa019cb380480e4800d 814d80aa817580ed0481a1813681c7818381ed81cf0Ba790cca6f1ba0B648d51a046bc0B8e a59ecaa0f10B81917bb262a10481f782b681a3823481ce81f60481b381a68127807280e4 80590B526f5bb95ece0480d681318126823d811782b80B7e8c7c9b6f9f0480ed82dd804d 826a8038825c0A816a0F> DC 87 /Wcursive <00831801802b7fd7835082dc02802e82460Ba297d6abe5730480a581f4806e80f7 805f80ae048056808480297ff3806a7fdb0B9b76b48ec5a004810b8060814f80dc81958153 0B7a5e733c6d1a04817480ab81618069815980260B7d67793a9b330481ef7fbd82c58175 82ec81c60Ba293c3a7e5bb0B658c539f47ba0483218251834d82e3831c82dc0482f382d5 8274823b82c981da0482b28191822c807681e880560B546b549f58bb0481ce80f4822e827c 822082c20B7d8c739667960481f282d8819682958185828a0B9971a55ca83f0481b28215 81a981c0819381900481708142812080c980ee80810B76715c5547660B708d76ae78bf04 80c3813c80ed81cf810382650B829190e179ee0B7c82768371810480c582c580518272802c 82590A826d0F> DC 88 /Xcursive <0082d2017fa27fb982a482de028074824b0A866b048093824d80d8828e80fc826304 81248233812081698122812304810180fa80398009800080020B717e678862950B75a27fce 8bee0B8da3a1c0bbdb0A778a047ff280c17fc980927fb38058047fa480307f947feb7fb4 7fc60B8f6ea874ba7e0480507ff980d980a58125810104812880bf81247fe8817a7fd40Ba9 76d99af6af0482378039826b8082828d80d50A4e76048245808a8221805381ef8025048179 804d818180f4817c815a03820b820a0B806883548c3e04823f81e2826b81f7829782090B5e 9757c458eb0482f883088257830a820d823d038179817b04817981bd81808283816582b80B 779066a252a304810a82dc808f82668074824b0F> DC 89 /Ycursive <0082710180377f2b82ba82e002803882680A836f0B968bbc9ed48c0480b982458098 81a8809381880480818128806680c3805880640B7e6c7b5580410B86629d52b94b048075 7fc080537f8a805a7f4f0B845d9354b0670480c07f5780f27f83811d7fb20481497fe28162 801e817c80590481d4811e823d823482ba82de04828782c9825482b6822082a30481ea821b 81b48191816d811104815780e98112808080f0806f0B7178607b57890B6d9f76cc7bee04 80d5817581218237810a82c40B7d9273a25f9a0480be82cf806082848038826802815680cd 0A837f0481308053810a7fbc809f7f6d0480897f96808c7fc2809c7fec0480e18014812e 8086815680cd0F> DC 90 /Zcursive <00824c017fbb7fba827582d902806782230Ab2870B8b9897b0aac404811a827e816d 825e81c4825c0380358081047f8d80407f9f7f7b80248034048072802e80a57fd480f27fbf 0481647fa181bc803381e080870A567a0B7a5f6c405925048158800f811b802d80eb80450B 5b9239aa13b90B7186658655810381f1825604822d8261829082b5827182d30B679a236013 500481c082ae817f82c8813d82d80B6e84627b54700480d2829a8097826280678223 0F> DC 91 /union <0083e80180bd7ff5832a828802832a82880946067e9c0482f080ea82e780aa 82be807e04828a8045823f802e81f4802e048155802e80f7808480f88124068164094606 7e9c0480bd806681377ff681f47ff50482b27ff6832a8065832a81240681640F> DC 92 /intersection <0083e80180bd8000832a82930280be800009ba0681640480f782048155 825a81f4825a04823f825a828a824382be820a0482e781de82f0819e82f08164067e9c09ba 06816404832a822282b1829381f48294048137829380bd822280be8164067e9c0F> DC 93 /unionmultiset <0083e80180bd7ff5832a828802832a82880946067e9c0482f080ea82e780aa 82be807e04828a8045823f802e81f4802e048155802e80f7808480f88124068164094606 7e9c0480bd806681377ff681f47ff50482b27ff6832a8065832a81240681640281db809609 b206809407809408b3077f6c068094094e067f6c077f6c084d078094067f6c0F> DC 94 /logicaland <0083e801807d7fb8836a829c02820d829c094e03807e7fb909bb0381f4825703 832f7fb909bb03820d829c0F> DC 95 /logicalor <0083e801807d7fb8836a829c0281db7fb909b203836a829c09450381f47ffe03 80b9829c09450381db7fb90F> DC 96 /turnstileleft <0082630180378000822b82ce028038800009b906814a0781bb08ba077e4506 814b0947067d310F> DC 97 /turnstileright <0082630180378000822b82ce02822c80000682cf0946067eb5077e46084607 81ba067eb609ba0F> DC 98 /bracketleftbt <0082100180e67f2581cb83080280e78308067c1e0780e408bf077f5e 0683a3093e0F> DC 99 /bracketrightbt <0082100180447f25812983080281298308093e067c5d077f5e084107 80e40683e20F> DC 100 /bracketlefttp <0082100180e67f0781cb82ea0280e77f0709c20683a30780a208c007 7f1c067c1d0F> DC 101 /bracketrighttp <0082100180447f07812982ea0281297f070683e3077f1c084007 80a2067c5d09c20F> DC 102 /braceleft <0081f40180557f14819d82fb0280dd7fbd0480dd7f2e81167f17819e7f15 089a04813c7f33812a7f50812b7faf06808b04812b80b3812080e980a381080481218126 812b815d812b81d506808c04812a82c0813d82dd819e82e2089a04811782fa80dd82e080dd 8253067f530480dd813c80bd81238056811708610480bd80eb80dd80d480dd8068067f55 0F> DC 103 /braceright <0081f40180557f14819d82fb0281167fbd0680ab04811680d4813680eb 819d80f8089f04813681238116813c811681a60680ad04811682e180de82f9805682fc0866 0480b682dd80c982c080c98261067f740480c9815d80d38126815081080480d380e980c9 80b380c9803a067f750480c97f5080b77f3380567f2f08660480de7f1781167f2e81167fbd 0F> DC 104 /angleleft <00814d01801c7f008131830f028108831003801c81080381087f010Aa992 038062810803813182fe0A57920F> DC 105 /angleright <00814d01801c7f008131830f02804583100A576e0380eb810803801c 7f130Aa96e038131810803804583100F> DC 106 /bar <00825a0181177f0f814183000281187f1009aa0683f00956067c100F> DC 107 /bardbl <0083e80181807f14826782fb02818082fc067c1909ba0683e7094602822e82fc 067c1909ba0683e709460F> DC 108 /arrowupdown <0081f40180577f14819b82fb0281167f8206830c03816981c20Ab395038120 82fc093403805881d70Ab36b0380de828e067cf403808b804e0A4d6a0380d47f1509cc03 819c80380A4d960381167f820F> DC 109 /arrowdblupdown <0081f40180237f1481cf82fb02816480140681e70Abd160Aae9c03810a82fc09 5f03802481ad0Aae640Abeea067e190A42ea0A52640380e97f1509a10381cf80620A529c0A 43160281317fbd0A49200A48e00682960Ab8e00Ab720067d6a0F> DC 110 /backslash <0081f40180297f1381cc82fc0281987f130Ab49403805e82fc0A4c6d038198 7f130F> DC 111 /wreathproduct <0081160180377fb680dc81f90280db7fb708a00B4585229913d404805d806f 8077809d80a180cf0480d6810e80ed814680d2819a0480bb81e1807d81fc803881f9085e0B b57fda6beb340480be813580908106805c80c904803380a28032804c803f801b0480567fca 808f7fba80db7fb70F> DC 112 /radical <0083e80180267c7e83ec80300281df7c7f09980383ed800908a70966038207 7cf00380df7f260380277ec80A8f610Aebb60381df7c7f0F> DC 113 /coproduct <008300018017800082ed82940280178294086c0Bc97be276e228067e450B8034 652c1e27086c0782d608940B3a851e8c1ed90681bb0B80ce9ad3e2d80894077ed1086c0Bc5 7ce171e227067e5704821f801b81e4802581928026048131802680e4801180e5807e0681a9 0B80cd9cd4e2d90894077ed00F> DC 114 /gradient <0082c90180177ff582b582940281707ff60382b68295077d6203815e7ff6 099202818a80940380a982680781c203818a80940F> DC 115 /integral <008112017fa77f4b816b82f502815482e30B61983396118604808782bb 80748241806981e5048059815c805c80d180578048048055801a80557fb6803a7f8e0B726c 5a6d4f820B759672ab55ae0B4586384061200Ba068cc69ee7a04808b7f86809e800080a9 805c0480b880e480b5816e80bb81f70480bd822480bd828b80d882b30B8d93a794b17d0B8b 6a9055ac530Bba7ac7c09fe00F> DC 116 /unionsqr <0083e80180bd8000832a828802832a82880946067db2077e0806824e094606 7d7807826c0682880F> DC 117 /intersectsqr <0083e80180bd8000832a828802832a8000068288077d94067d7809ba06824e07 81f8067db209ba0F> DC 118 /reflsubsetsq <0083e80180b57f85833d828a02833e801e08ba077db20681f907824e08b907 7d78067d940782880280b67f8607828808b9077d7808470F> DC 119 /reflsupersetsq <0083e80180b57f85833d828a0280b6801e07828806826c077d78084707824e06 7e07077db2084602833e7f8608b9077d7808470782880F> DC 120 /section <0081f40180387f8381bb82c30280e7805f04810c803f814d800f81407fd704 81347f9d80e87f9080b87fa40B5d906d9f7eb20B98998ac36acd048045803d80307f9a80cb 7f860481137f7c81757f9581887fe504819a802d81608064812e80900481638090819a80a7 81b180d90481d28125819d8169816681980A2aca0480e6820580ab823280b3826f0B88b4c1 c3edb60Bd964503593050Ba863dc89d8b604818582a5813f82c3810282c30480b582c38065 82938069823e04806c8201809c81d980c581b304809181b2805c819c8044816b0480208120 805880da808f80ab0Ad83402808f81220B60b06af3adf80480f4819f814a814a8165812004 818980e8816f809f812680aa0480f980b080a780fe808f81220F> DC 121 /dagger <0081f401802b7f7381c882c30280bf81190480e3807280ea801c80ee7f7409 9904810880018112808f8135811904811481518106818c810581cd0Bcc78d260fe580Ba279 c68bc5b00B7ea75cb939b10B4f75445e045b0B809d81b989d40B899c98b49fd00B8aa16ebe 4ebe0B5e8142644c420480dd823780ef824380ef81e10B4083359a04a50B5d883a76394f0B 7f5ba349c5500Bac88b4a1fea80480ee818c80e0815180bf81190F> DC 122 /daggerdbl <0081f401802b7f6e81c882c30280ec81c90480ef818a80de814e80bf8118 0480e080e080eb80a880ee80670B39862f9d02a50B5e873b753c500B815aa347c64f0Baf8b bf9ffaa30480ed7fe580df800180c77fae0B775e9141b2410Ba280be9cb4bf0B79986cae64 c60B789d77bc76da0Bca7bc868fa5d0Ba378c58ac7b10B81a55eb73db00B5378335a035c04 810480a6811680e381358118048115814f8108818b810681cb0Bc779d062fe5a0Ba279c58b c4b00B7ea65db93ab10B51764061065d048106824c81168231812d82840B8aa26ebf4ebf0B 5e8142644c410480e0822d80ea825480ed81e30B3c84369806a30B5d883a76394f0B7f5ba2 49c3500Bae88caa5fda40F> DC 123 /paragraph <0081f40180207f9181d382b60281d482b6077f0c04807a82b68020827b 8020820c04802081d9803781a8806081880Ba365cb5ef65b067e2f09b70682fa09d6067d06 09b60682fa09bb08aa0F> DC 124 /clubsuit <00847d0180687f88841382ff02825c809e08df04829c80f682bd80b282ea808c 04836580248413807b8413811b04841381bc8365821282ea81aa0482be8185829c8140825c 813904825b818382a381a482cd81d7048335825282df82ff823e830004819d82ff81478251 81af81d70481db81a282218185822081390481e1814081be8185819281aa04811782128069 81bc8069811b048069807a811780248192808c0481bf80b281e080f6822080fd048220806b 8224800181c87f880482167f9982667f9982b47f880482777fd9825c8038825c809e 0F> DC 125 /diamondsuit <00847c0180887f8983f3831c02823e7f8a0482de804e833480a883f3815204 833c81f882db825d823e831c0481a18261813c81f7808981520480d5810c812280c7816a 807c0481b4802e81f97fdc823e7f8a02823f7fcb0481ba806a816380c580cb8152048165 81e081b98239823f82db0482c48235831481e183b2815204831280c282c58071823f7fcb 0F> DC 126 /heartsuit <00847b0180637f7f841782f802823d82750481be8372804a82ed806581c204 8075810d811f80c381a080610481f7802082207fe982337f7f09940482577fda827d8018 82c6805204834a80bb84058104841681c204843282ed82bb8372823d827502823d7fea04 81f880bf809d80d5809481da04808f826b810582e4819982c30481f582b0821a82638230 8211099b0482608263828682b082e282c304837682e483ec826b83e781da0483dd80d7827b 80b5823d7fea0F> DC 127 /spadesuit <00847c0180a07f8083db82fc0282578088048278805982a0803382db802504 8352800983c6806183d880d704840381e682868201824582fd09720481f381fd807981e8 80a480d70480b68067811f8011819280220481d3802c820080558225808804822680268212 7fd381dc7f8004821f7f8a825d7f8a82a07f8004826a7fd382558026825780880F> DC 160 /minus <00834101807b810d82c5814702807c810d07824908ba077db708460F> DC 161 /dotmath <00823c0180dd810e815e818e0280e381660B6133d602f6500Ba0ce29fe0ab0 0F> DC 162 /multiply <008341018094801a82b382390280bd801b0381a4810203828b801b0Aa8a8 0381cc812a0382b382110A58a80381a481520380bd823a0A585703817c812a03809580430A a8580F> DC 163 /asteriskmath <0083e8018140806182a781f30281ee81350B3caa4db222db0B6c9347 9c367f0B6f638848a23f0481a0813d81a3815081e8812a0B375a3b6d025d0B64784b5d5c3f 0B8f64b46bc87d0Baaa6a1b8e0dd0B7c2d6e3b60020B79638240a53f0Ba080ada3a7be04 820e80d781fb80d281fa81200Bc355b24fdd250B956cb963ca800B909c79b95fc1048249 8117824381058200812a0Bcba7c393fea40B9c87b4a2a4c00B709c4c9637830B565a614921 240B83d192c59ffd0B879d7ec05bc10B6080545e59420481da817c81ec818481ee8135 0F> DC 164 /divide <00834101807b803a82c5821902816a81f40B6238cf0bee530B9dc82ff612ad 02807c810d07824908ba077db7084602816a808c0B6239cf0cee540B9dc72ef412ac 0F> DC 165 /diamondop <0081f4018006801081ed81f602800781030380fa80100381ed81030380fa81f6 038007810302803e81030380fa81bf0381b681040380f8804803803e81030F> DC 166 /plusminus <00834101807b800082c582830281be817b0681080946067ef8077ef80847 078108067ef8077ef8084607824908ba077ef906810807810708b9077ef90F> DC 167 /minusplus <00834101807b800082c582830281be810807810708ba077ef906810707810708 ba077db70846078108067ef9077ef80846078108067ef809ba0681080F> DC 168 /circleplus <0083e80180727fa9837682ac0283468142077ec50681380482ac8274833f81e3 834681420281dc8142077ec60480b281e98133826d81dc827a067ec80280a2811307813a06 7ec80481347fe680b2806d80a2811302820b811307813b04833d80c3831e807882e5803e04 82ab8005825e7fdb820b7fdb0681380281f482ac04812282ac807381fc8073812a048072 805681207faa81f47faa0482c97faa837680568376812a04837681fd82c782ac81f482ac 0F> DC 169 /circleminus <0083e80180727fa9837582ac028344811304832a7f8c80de7f5980a4811307 82a00280a581420480cf82ed832782d883448142077d61028376812a04837581fe82c782ab 81f482ac04812082ac807381fe8072812a0480728056811f7faa81f47fa90482c87fa98376 80568376812a0F> DC 170 /circlemultiply <0083e80180727faa837582ab028305823b04827082d1817982d080e4823b04 804f81a7804f80ae80e4801a04817a7f85826e7f868305801a04839b80b0839a81a58305 823b0281f4810a0382d2802c0482937ffc824a7fdb81f87fdb0481a77fdb81517ff38116 802d0381f4810a0280f582090381d3812b0380f6804e04808280cb808d818980f5820902 81f4814c038115822a04819582948252829682d182290381f4814c0282f3804c038214812b 0382f2820804835f8192836180c382f3804c0F> DC 171 /circledivide <0083e80180727fa9837582ab0280e480190481797f85826f7f868305801904 839980ae839981a68305823a04826f82d1817a82d180e4823a04804f81a6804f80ae80e4 80190280f7804d047ff58176816d833582d182270380f7804d0282f28207048363817b8366 80be82e2803b0482657fbf819b7fb98117802c0382f282070F> DC 172 /circledot <0083e80180727fa9837682ac0280a3812a0480a281e2813c827c81f4827c04 82ac827b834581e28345812a048345807382ac7fda81f47fda04813b7fda80a3807180a3 812a0281b3812a0481b380d6823480d58234812a048234817e81b3817e81b3812a0281f4 82ac04812282ac807381fc8073812a048072805681207faa81f47fa90482c77fa983768057 8376812a04837681fc82c782ac81f482ac0F> DC 173 /overlaycircle <0083e8017fff7f1483e782fb028031810804803081fe80fc82ca81f282ca04 82e982ca83b581ff83b581080483b5801282e97f4681f27f460480fd7f46803180128031 81080281f382fc0480e182fb8000821a800081070480007ff580e07f1581f37f15048306 7f1583e77ff583e781070483e7821a830682fc81f382fc0F> DC 174 /circleop <0081f4018036804081bb81c5028070818c0480258141802580c48070807904 80ba802f8137802e818280790481cd80c581ce81428182818d04813781d880ba81d78070 818c02808b81700480c681ac812a81ac816681710481a2813581a180d28166809604812a 805980c7805a808c809604804f80d180508135808b81700F> DC 175 /bullet <0081f4018036804081bb81c5028070818c0480258141802580c48070807904 80ba802f8137802e818280790481cd80c581ce81428182818d04813781d880ba81d78070 818c0F> DC 176 /hardyequiv <0083e80180ce8075831881df0280e781df0A685104817f812c8269812d8319 81b00A68af04826881668180816580e781df0280e7807504818180ef826780ee830180750A 98af04826881278180812880cf80a40A98510F> DC 177 /equivalence <0083e80180cf8069831881ea0280cf806a07824a08b9077db6084702 80cf810d07824a08ba077db608460280cf81b107824a08ba077db608460F> DC 178 /reflexsubset <0083e80180aa7f85833d828a02833e801e08ba077e9b04813a8058 80e480b580e481540480e481a080fb81ea8134821f0481608247819f825081d98251078165 08b9077e9b04811b828a80aa821280aa81540480aa8097811b801e81d9801e0781650280b2 7f8607828c08b9077d7408470F> DC 179 /reflexsuperset <0083e80180b37f858347828a0280b3801e0781650482d6801e8347 809783478154048347821182d6828a8218828a077e9b08470781650482b88250830d81f4 830d815404830d80b582b8805882188058077e9b084602833f7f8608b9077d74084707828c 0F> DC 180 /lessequal <0083e80180cf80178318823c0280d18146038319808f08ba038126816603 8319820208ba0380d181840842028319801808ba077db6084607824a0F> DC 181 /greaterequal <0083e80180cf80178318823c0280cf801807824a08ba077db6084602 8317814608be0380cf823c08460382c281660380cf80c9084603831781460F> DC 182 /precedesequal <0083e80180cf80008318826e028319800008ba077db6084607824a0280d08181 0849048144814981bc8141822b811d04829680fa82c480c482e4805d0Ab28e04830080b0 82e580f182a6811a048254815181f1815e819081660481f1816e8254817b82a681b20482e4 81dc8301821c831682610A4e8e0482c58209829481d0822c81ae0481bd818a8145818280d0 81810F> DC 183 /followsequal <0083e80180cf80008318826e02831881810482a38182822b818a81bc81ae04 815481d0812382098104826f0A4e720480e7821c810481dd814281b2048194817b81f7816e 825881660481f7815e819481518142811a04810380f180e780b080d2806b0Ab272048124 80c4815280fa81bd811d04822c814182a481498318814a08b70280cf800007824a08ba07 7db608460F> DC 184 /similar <0083e80180aa80e3833d81720280aa80e404811a81308160814681e5 811a04827f80e782b080d8833e813308bf0482ab810b828b812081e7815304816b817b8116 816680aa812208420F> DC 185 /approxequal <0083e80180aa8093833d81c00280aa809404811a80e0816080f681e5 80ca04827f809782b08088833e80e308bf0482a980ba828b80d081e7810304816b812b8116 811680aa80d208420280aa813204811a817f8160819581e5816904827f813682b08126833e 818208bf0482aa815a828b816e81e781a104816b81ca811681b480aa817108410F> DC 186 /propersubset <0083e80180aa8007833d827402833e800808ba077e9b04813a8042 80e4809f80e4813e0480e4818a80fb81d4813482090481608231819f823a81d9823b078165 08b9077e9b04811b827480aa81fc80aa813e0480aa8081811b800881d98008078165 0F> DC 187 /propersuperset <0083e80180aa8007833d82740280aa82740847078165048249823a 8288823182b482090482ed81d48304818a8304813e048304809f82ae8042820f8042077e9b 08460781650482cd8008833d8081833e813e04833d81fc82cc8274820f8274077e9b 0F> DC 188 /muchless <0083e80180377fb783b082590280378122084d0382627fb708bc038085810803 8262821e08bc03803781220281868122084d0383b17fb708bc0381d381080383b1821e08bc 03818681220F> DC 189 /muchgreater <0083e80180377fb783b082590283b18122038186825a08440383638108038186 7ff308440383b180ef08b30282628122038037825a084403821581080380377ff3084403 826280ef08b30F> DC 190 /precedes <0083e80180cf8022831582340280d081470849048144810f81bc8107822b80e3 04829680c082c4808a82e480220Ab28f048300807682e580b782a680e0048254811781f1 81248190812c0481f181348254814082a681780482e481a2830181e1831682260A4e8e04 82c581cf82948196822c81740481bd81508145814780d081470F> DC 191 /follows <0083e80180cf80228315823402831681470482a181478229815081b9817404 81518196812181cf810282340A4e720480e581e1810281a2813f8178048192814081f58134 8255812c0481f5812481928117813f80e004810180b780e5807680d080310Ab271048122 808a815080c081ba80e304822a810782a1810f8316811008b70F> DC /FontBBox {-213 -898 1047 796} def end /Dutch801-Roman-DECmath_Symbol bsd definefont pop %%EndFont DEC_WRITE_dict begin loads version cvi 23.0 gt { currentdict {dup type /arraytype eq {bind def} {pop pop} ifelse} forall} if 0.0100 0.0100 s %%EndSetup %%Page: 1 1 /$P a D g N 0 79200 T S R S 6313 -23156 T N 0 G 300 -1050 M /Times-Italic-ISOLatin1 $ /Times-Italic & P /Times-Italic-ISOLatin1 F 1000 o f 2.3 0 32 (This paper is a revised version of an article by the same) W 300 -2150 M 27.2 0 32 (title and author which appeared in the April 1991 issue) W 300 -3250 M (of ) h /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f (Communications of the ACM.) h 300 -4500 M 300 -6400 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1200 o f (Abstract) h 300 -8150 M /Times-Roman-ISOLatin1 F 1000 o f 135.1 0 32 (For the past few years, a joint ISO/CCITT committee) W 300 -9250 M 258.8 0 32 (known as JPEG \(Joint Photographic Experts Group\)) W 300 -10350 M 281.4 0 32 (has been working to establish the first international) W 300 -11450 M 110.6 0 32 (compression standard for continuous\255tone still images,) W 300 -12550 M 190.4 0 32 (both grayscale and color. JPEG's proposed standard) W 300 -13650 M 401.1 0 32 (aims to be generic, to support a wide variety of) W 300 -14750 M 189.5 0 32 (applications for continuous\255tone images. To meet the) W 300 -15850 M 587.7 0 32 (differing needs of many applications, the JPEG) W 300 -16950 M 23.0 0 32 (standard includes two basic compression methods, each) W 300 -18050 M 23.6 0 32 (with various modes of operation. A DCT\255based method) W 300 -19150 M 127.0 0 32 (is specified for ) W 127.0 0 32 (\026) W 127.0 0 32 (lossy'' compression, and a predictive) W 300 -20250 M 166.6 0 32 (method for ) W 166.6 0 32 (\026) W 166.6 0 32 (lossless'' compression. JPEG features a) W 300 -21350 M 86.9 0 32 (simple lossy technique known as the Baseline method,) W 300 -22450 M 163.1 0 32 (a subset of the other DCT\255based modes of operation.) W 300 -23550 M 107.9 0 32 (The Baseline method has been by far the most widely) W 300 -24650 M 72.5 0 32 (implemented JPEG method to date, and is sufficient in) W 300 -25750 M 141.8 0 32 (its own right for a large number of applications. This) W 300 -26850 M 52.1 0 32 (article provides an overview of the JPEG standard, and) W 300 -27950 M (focuses in detail on the Baseline method.) h 300 -29050 M 300 -30150 M 300 -31400 M /Times-Bold-ISOLatin1 F 1200 o f (1 Introduction) h 300 -33150 M /Times-Roman-ISOLatin1 F 1000 o f 298.8 0 32 (Advances over the past decade in many aspects of) W 300 -34250 M 499.8 0 32 (digital technology \255 especially devices for image) W 300 -35350 M 203.3 0 32 (acquisition, data storage, and bitmapped printing and) W 300 -36450 M 337.0 0 32 (display \255 have brought about many applications of) W 300 -37550 M 13.6 0 32 (digital imaging. However, these applications tend to be) W 300 -38650 M 117.1 0 32 (specialized due to their relatively high cost. With the) W 300 -39750 M 126.7 0 32 (possible exception of facsimile, digital images are not) W 300 -40850 M 291.3 0 32 (commonplace in general\255purpose computing systems) W 300 -41950 M 30.6 0 32 (the way text and geometric graphics are. The majority) W 300 -43050 M 3.9 0 32 (of modern business and consumer usage of photographs) W 300 -44150 M 229.1 0 32 (and other types of images takes place through more) W 300 -45250 M (traditional analog means.) h 300 -46350 M 300 -47450 M -6313 23156 T R S 31919 -23173 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 F 1000 o f 305.4 0 32 (The key obstacle for many applications is the vast) W 300 -2150 M 215.3 0 32 (amount of data required to represent a digital image) W 300 -3250 M 107.9 0 32 (directly. A digitized version of a single, color picture) W 300 -4350 M 144.8 0 32 (at TV resolution contains on the order of one million) W 300 -5450 M 55.0 0 32 (bytes; 35mm resolution requires ten times that amount. ) W 300 -6550 M 171.9 0 32 (Use of digital images often is not viable due to high) W 300 -7650 M 31.7 0 32 (storage or transmission costs, even when image capture) W 300 -8750 M (and display devices are quite affordable.) h 300 -9850 M 300 -10950 M 661.0 0 32 (Modern image compression technology offers a) W 300 -12050 M 533.0 0 32 (possible solution. State\255of\255the\255art techniques can) W 300 -13150 M 463.9 0 32 (compress typical images from 1/10 to 1/50 their) W 300 -14250 M 427.4 0 32 (uncompressed size without visibly affecting image) W 300 -15350 M 372.4 0 32 (quality. But compression technology alone is not) W 300 -16450 M 309.5 0 32 (sufficient. For digital image applications involving) W 300 -17550 M 490.5 0 32 (storage or transmission to become widespread in) W 300 -18650 M 355.6 0 32 (today's marketplace, a standard image compression) W 300 -19750 M 675.7 0 32 (method is needed to enable interoperability of) W 300 -20850 M 152.8 0 32 (equipment from different manufacturers. The CCITT) W 300 -21950 M 259.0 0 32 (recommendation for today's ubiquitous Group 3 fax) W 300 -23050 M 40.2 0 32 (machines [17] is a dramatic example of how a standard) W 300 -24150 M 268.3 0 32 (compression method can enable an important image) W 300 -25250 M 45.0 0 32 (application. The Group 3 method, however, deals with) W 300 -26350 M 75.1 0 32 (bilevel images only and does not address photographic) W 300 -27450 M (image compression.) h 300 -28550 M 300 -29650 M 107.8 0 32 (For the past few years, a standardization effort known) W 300 -30750 M 134.6 0 32 (by the acronym JPEG, for Joint Photographic Experts) W 300 -31850 M 134.7 0 32 (Group, has been working toward establishing the first) W 300 -32950 M 305.2 0 32 (international digital image compression standard for) W 300 -34050 M 978.0 0 32 (continuous\255tone \(multilevel\) still images, both) W 300 -35150 M 158.4 0 32 (grayscale and color. The ) W 158.4 0 32 (\026) W 158.4 0 32 (joint) W 158.4 0 32 (\027) W 158.4 0 32 ( in JPEG refers to a) W 300 -36250 M 643.2 0 32 (collaboration between CCITT and ISO. JPEG) W 300 -37350 M 231.3 0 32 (convenes officially as the ISO committee designated) W 300 -38450 M 588.2 0 32 (JTC1/SC2/WG10, but operates in close informal) W 300 -39550 M 86.4 0 32 (collaboration with CCITT SGVIII. JPEG will be both) W 300 -40650 M 86.6 0 32 (an ISO Standard and a CCITT Recommendation. The) W 300 -41750 M (text of both will be identical.) h 300 -42850 M 300 -43950 M 166.0 0 32 (Photovideotex, desktop publishing, graphic arts, color) W 300 -45050 M 180.3 0 32 (facsimile, newspaper wirephoto transmission, medical) W 300 -46150 M 610.6 0 32 (imaging, and many other continuous\255tone image) W 300 -47250 M 67.4 0 32 (applications require a compression standard in order to) W -31919 23173 T R S 6519 -10545 T N 0 G 8366 -1350 M /Helvetica-Bold-ISOLatin1 $ /Helvetica-Bold & P /Helvetica-Bold-ISOLatin1 F 1400 o f (The JPEG Still Picture Compression Standard) h 300 -2550 M 20016 -3650 M /Helvetica-ISOLatin1 $ /Helvetica & P /Helvetica-ISOLatin1 F 1000 o f (Gregory K. Wallace) h 19156 -4750 M (Multimedia Engineering) h 17596 -5850 M (Digital Equipment Corporation) h 18866 -6950 M (Maynard, Massachusetts) h 300 -7888 M 300 -9373 M 5659 -10420 M /Times-Italic-ISOLatin1 F 1000 o f (Submitted in December 1991 for publication in IEEE Transactions on Consumer Electronics) h 300 -11358 M 300 -12628 M -6519 10545 T R S 30679 -75546 M /Times-Roman-ISOLatin1 F 1000 o f (1) h R showpage $P e %%Page: 2 2 /$P a D g N 0 79200 T S R S 6337 -7200 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 71.1 0 32 (develop significantly beyond their present state. JPEG) W 300 -2150 M 345.0 0 32 (has undertaken the ambitious task of developing a) W 300 -3250 M 472.2 0 32 (general\255purpose compression standard to meet the) W 300 -4350 M 738.2 0 32 (needs of almost all continuous\255tone still\255image) W 300 -5450 M (applications.) h 300 -6550 M 300 -7650 M 141.9 0 32 (If this goal proves attainable, not only will individual) W 300 -8750 M 254.5 0 32 (applications flourish, but exchange of images across) W 300 -9850 M 182.3 0 32 (application boundaries will be facilitated. This latter) W 300 -10950 M 305.5 0 32 (feature will become increasingly important as more) W 300 -12050 M 5.6 0 32 (image applications are implemented on general\255purpose) W 300 -13150 M 288.4 0 32 (computing systems, which are themselves becoming) W 300 -14250 M 377.8 0 32 (increasingly interoperable and internetworked. For) W 300 -15350 M 240.7 0 32 (applications which require specialized VLSI to meet) W 300 -16450 M 1208.0 0 32 (their compression and decompression speed) W 300 -17550 M 832.8 0 32 (requirements, a common method will provide) W 300 -18650 M 519.4 0 32 (economies of scale not possible within a single) W 300 -19750 M (application. ) h 300 -20850 M 300 -21950 M 305.4 0 32 (This article gives an overview of JPEG's proposed) W 300 -23050 M 299.8 0 32 (image\255compression standard. Readers without prior) W 300 -24150 M 400.6 0 32 (knowledge of JPEG or compression based on the) W 300 -25250 M 222.5 0 32 (Discrete Cosine Transform \(DCT\) are encouraged to) W 300 -26350 M 368.7 0 32 (study first the detailed description of the Baseline) W 300 -27450 M 333.2 0 32 (sequential codec, which is the basis for all of the) W 300 -28550 M 31.7 0 32 (DCT\255based decoders. While this article provides many) W 300 -29650 M 34.9 0 32 (details, many more are necessarily omitted. The reader) W 300 -30750 M 409.9 0 32 (should refer to the ISO draft standard [2] before) W 300 -31850 M (attempting implementation.) h 300 -32950 M 300 -34050 M 270.4 0 32 (Some of the earliest industry attention to the JPEG) W 300 -35150 M 170.6 0 32 (proposal has been focused on the Baseline sequential) W 300 -36250 M 95.6 0 32 (codec as a motion image compression method \255 of the) W 300 -37350 M 108.3 0 32 (``intraframe'' class, where each frame is encoded as a) W 300 -38450 M 208.1 0 32 (separate image. This class of motion image coding,) W 300 -39550 M 261.0 0 32 (while providing less compression than ``interframe'') W 300 -40650 M 190.1 0 32 (methods like MPEG, has greater flexibility for video) W 300 -41750 M 147.0 0 32 (editing. While this paper focuses only on JPEG as a) W 300 -42850 M 65.6 0 32 (still picture standard \(as ISO intended\), it is interesting) W 300 -43950 M 211.0 0 32 (to note that JPEG is likely to become a ``de facto'') W 300 -45050 M (intraframe motion standard as well.) h 300 -46150 M 300 -47250 M 300 -48500 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1200 o f 195.7 0 32 (2 Background: Requirements and Selec\255) W 300 -49800 M (tion Process) h 300 -51550 M /Times-Roman-ISOLatin1 F 1000 o f 492.9 0 32 (JPEG's goal has been to develop a method for) W 300 -52650 M 249.6 0 32 (continuous\255tone image compression which meets the) W 300 -53750 M (following requirements:) h 300 -54850 M 300 -55950 M (1\)) h 2100 -55950 M 217.7 0 32 (be at or near the state of the art with regard to) W 2100 -57050 M 841.5 0 32 (compression rate and accompanying image) W 2100 -58150 M 11.0 0 32 (fidelity, over a wide range of image quality ratings,) W 2100 -59250 M 59.6 0 32 (and especially in the range where visual fidelity to) W 2100 -60350 M 326.3 0 32 (the original is characterized as ) W 326.3 0 32 (\026) W 326.3 0 32 (very good) W 326.3 0 32 (\027) W 326.3 0 32 ( to) W 2100 -61450 M 951.0 0 32 (\026) W 951.0 0 32 (excellent) W 951.0 0 32 (\027) W 951.0 0 32 (; also, the encoder should be) W 2100 -62550 M 214.0 0 32 (parameterizable, so that the application \(or user\)) W 2100 -63650 M (can set the desired compression/quality tradeoff;) h -6337 7200 T R S 31919 -7200 T N 0 G 2100 -1050 M 2100 -2150 M 300 -3250 M /Times-Roman-ISOLatin1 F 1000 o f (2\)) h 2100 -3250 M 838.7 0 32 (be applicable to practically any kind of) W 2100 -4350 M 70.0 0 32 (continuous\255tone digital source image \(i.e. for most) W 2100 -5450 M 215.0 0 32 (practical purposes not be restricted to images of) W 2100 -6550 M 489.8 0 32 (certain dimensions, color spaces, pixel aspect) W 2100 -7650 M 0.4 0 32 (ratios, etc.\) and not be limited to classes of imagery) W 2100 -8750 M 639.5 0 32 (with restrictions on scene content, such as) W 2100 -9850 M 856.2 0 32 (complexity, range of colors, or statistical) W 2100 -10950 M (properties;) h 2100 -12050 M 300 -13150 M (3\)) h 2100 -13150 M 128.6 0 32 (have tractable computational complexity, to make) W 2100 -14250 M 549.5 0 32 (feasible software implementations with viable) W 2100 -15350 M 348.0 0 32 (performance on a range of CPU's, as well as) W 2100 -16450 M 400.8 0 32 (hardware implementations with viable cost for) W 2100 -17550 M (applications requiring high performance;) h 2100 -18650 M 300 -19750 M (4\)) h 2100 -19750 M ( have the following modes of operation:) h 2100 -20850 M 2100 -21950 M /Symbol F 1000 o f (\267) h 3900 -21950 M /Times-Roman-ISOLatin1 F 1000 o f 7.4 0 32 (Sequential encoding: each image component is) W 3900 -23050 M 35.0 0 32 (encoded in a single left\255to\255right, top\255to\255bottom) W 3900 -24150 M (scan;) h 3900 -25250 M 2100 -26350 M /Symbol F 1000 o f (\267) h 3900 -26350 M /Times-Roman-ISOLatin1 F 1000 o f 47.8 0 32 (Progressive encoding: the image is encoded in) W 3900 -27450 M 573.8 0 32 (multiple scans for applications in which) W 3900 -28550 M 404.0 0 32 (transmission time is long, and the viewer) W 3900 -29650 M 8.0 0 32 (prefers to watch the image build up in multiple) W 3900 -30750 M (coarse\255to\255clear passes;) h 3900 -31850 M 2100 -32950 M /Symbol F 1000 o f (\267) h 3900 -32950 M /Times-Roman-ISOLatin1 F 1000 o f 260.7 0 32 (Lossless encoding: the image is encoded to) W 3900 -34050 M 486.2 0 32 (guarantee exact recovery of every source) W 3900 -35150 M 76.7 0 32 (image sample value \(even though the result is) W 3900 -36250 M 607.2 0 32 (low compression compared to the lossy) W 3900 -37350 M (modes\);) h 3900 -38450 M 2100 -39550 M /Symbol F 1000 o f (\267) h 3900 -39550 M /Times-Roman-ISOLatin1 F 1000 o f 11.2 0 32 (Hierarchical encoding: the image is encoded at) W 3900 -40650 M 279.5 0 32 (multiple resolutions so that lower\255resolution) W 3900 -41750 M 75.7 0 32 (versions may be accessed without first having) W 3900 -42850 M (to decompress the image at its full resolution.) h 300 -43950 M 300 -45050 M 341.1 0 32 (In June 1987, JPEG conducted a selection process) W 300 -46150 M 400.6 0 32 (based on a blind assessment of subjective picture) W 300 -47250 M 194.3 0 32 (quality, and narrowed 12 proposed methods to three. ) W 300 -48350 M 87.3 0 32 (Three informal working groups formed to refine them,) W 300 -49450 M 55.5 0 32 (and in January 1988, a second, more rigorous selection) W 300 -50550 M 135.1 0 32 (process [19] revealed that the ) W 135.1 0 32 (\026) W 135.1 0 32 (ADCT) W 135.1 0 32 (\027) W 135.1 0 32 ( proposal [11],) W 300 -51650 M 129.6 0 32 (based on the 8x8 DCT, had produced the best picture) W 300 -52750 M (quality.) h 300 -53850 M 300 -54950 M 24.4 0 32 (At the time of its selection, the DCT\255based method was) W 300 -56050 M 444.3 0 32 (only partially defined for some of the modes of) W 300 -57150 M 114.6 0 32 (operation. From 1988 through 1990, JPEG undertook) W 300 -58250 M 161.5 0 32 (the sizable task of defining, documenting, simulating,) W 300 -59350 M 59.1 0 32 (testing, validating, and simply agreeing on the plethora) W 300 -60450 M 277.8 0 32 (of details necessary for genuine interoperability and) W 300 -61550 M 315.6 0 32 (universality. Further history of the JPEG effort is) W 300 -62650 M (contained in [6, 7, 9, 18].) h 300 -63750 M -31919 7200 T R S 30717 -74731 M /Times-Roman-ISOLatin1 F 1000 o f (2) h R showpage $P e %%Page: 3 3 /$P a D g N 0 79200 T S R S 6337 -7200 T N 0 G 300 -1200 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1200 o f (3 Architecture of the Proposed Standard) h 300 -2950 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 281.7 0 32 (The proposed standard contains the four ) W 281.7 0 32 (\026) W 281.7 0 32 (modes of) W 300 -4050 M 146.7 0 32 (operation) W 146.7 0 32 (\027) W 146.7 0 32 ( identified previously. For each mode, one) W 300 -5150 M 67.9 0 32 (or more distinct codecs are specified. Codecs within a) W 300 -6250 M 62.6 0 32 (mode differ according to the precision of source image) W 300 -7350 M 76.3 0 32 (samples they can handle or the entropy coding method) W 300 -8450 M 103.4 0 32 (they use. Although the word codec \(encoder/decoder\)) W 300 -9550 M 12.2 0 32 (is used frequently in this article, there is no requirement) W 300 -10650 M 43.3 0 32 (that implementations must include both an encoder and) W 300 -11750 M 246.4 0 32 (a decoder. Many applications will have systems or) W 300 -12850 M (devices which require only one or the other.) h 300 -13950 M 300 -15050 M 132.0 0 32 (The four modes of operation and their various codecs) W 300 -16150 M 159.8 0 32 (have resulted from JPEG's goal of being generic and) W 300 -17250 M 15.7 0 32 (from the diversity of image formats across applications. ) W 300 -18350 M 535.4 0 32 (The multiple pieces can give the impression of) W 300 -19450 M 300.5 0 32 (undesirable complexity, but they should actually be) W 300 -20550 M 0.3 0 32 (regarded as a comprehensive ) W 0.3 0 32 (\026) W 0.3 0 32 (toolkit) W 0.3 0 32 (\027) W 0.3 0 32 ( which can span a) W 300 -21650 M 24.1 0 32 (wide range of continuous\255tone image applications. It is) W 300 -22750 M 166.0 0 32 (unlikely that many implementations will utilize every) W 300 -23850 M 114.3 0 32 (tool \255\255 indeed, most of the early implementations now) W 300 -24950 M 187.8 0 32 (on the market \(even before final ISO approval\) have) W 300 -26050 M (implemented only the Baseline sequential codec.) h 300 -27150 M 300 -28250 M 111.1 0 32 (The Baseline sequential codec is inherently a rich and) W 300 -29350 M 593.8 0 32 (sophisticated compression method which will be) W 300 -30450 M 15.3 0 32 (sufficient for many applications. Getting this minimum) W 300 -31550 M 1291.0 0 32 (JPEG capability implemented properly and) W 300 -32650 M 629.2 0 32 (interoperably will provide the industry with an) W 300 -33750 M 360.8 0 32 (important initial capability for exchange of images) W 300 -34850 M (across vendors and applications.) h 300 -35950 M 300 -37050 M 300 -38300 M /Times-Bold-ISOLatin1 F 1200 o f (4 Processing Steps for DCT\255Based Coding) h 300 -40050 M /Times-Roman-ISOLatin1 F 1000 o f 138.7 0 32 (Figures 1 and 2 show the key processing steps which) W 300 -41150 M 232.8 0 32 (are the heart of the DCT\255based modes of operation. ) W 300 -42250 M 953.7 0 32 (These figures illustrate the special case of) W 300 -43350 M 55.6 0 32 (single\255component \(grayscale\) image compression. The) W 300 -44450 M 731.7 0 32 (reader can grasp the essentials of DCT\255based) W 300 -45550 M 851.2 0 32 (compression by thinking of it as essentially) W 300 -46650 M 236.1 0 32 (compression of a stream of 8x8 blocks of grayscale) W 300 -47750 M 86.6 0 32 (image samples. Color image compression can then be) W 300 -48850 M 372.0 0 32 (approximately regarded as compression of multiple) W 300 -49950 M 60.5 0 32 (grayscale images, which are either compressed entirely) W 300 -51050 M 475.8 0 32 (one at a time, or are compressed by alternately) W 300 -52150 M (interleaving 8x8 sample blocks from each in turn.) h 300 -53250 M 300 -54350 M 226.7 0 32 (For DCT sequential\255mode codecs, which include the) W 300 -55450 M 433.0 0 32 (Baseline sequential codec, the simplified diagrams) W 300 -56550 M (indicate how single\255component compression works in a ) h 300 -57650 M 132.6 0 32 (fairly complete way. Each 8x8 block is input, makes) W 300 -58750 M 44.9 0 32 (its way through each processing step, and yields output) W 300 -59850 M 222.0 0 32 (in compressed form into the data stream. For DCT) W 300 -60950 M 125.2 0 32 (progressive\255mode codecs, an image buffer exists prior) W 300 -62050 M 219.3 0 32 (to the entropy coding step, so that an image can be) W 300 -63150 M 21.4 0 32 (stored and then parceled out in multiple scans with suc\255) W 300 -64250 M 39.4 0 32 (cessively improving quality. For the hierarchical mode) W -6337 7200 T R S 31919 -7200 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 F 1000 o f 315.8 0 32 (of operation, the steps shown are used as building) W 300 -2150 M (blocks within a larger framework.) h 300 -3250 M 300 -4950 M /Times-Bold-ISOLatin1 F 1000 o f (4.1 8x8 FDCT and IDCT) h 300 -6650 M /Times-Roman-ISOLatin1 F 1000 o f 111.1 0 32 (At the input to the encoder, source image samples are) W 300 -7750 M 7.6 0 32 (grouped into 8x8 blocks, shifted from unsigned integers) W 300 -8850 M 219.3 0 32 (with range [0, 2) W n 0.800 o f 0.0 448.0 m 219.3 0 32 (P) W 0 -448.0 m n 1.250 o f 219.3 0 32 ( \255 1] to signed integers with range) W 300 -9950 M 65.8 0 32 ([\2552) W n 0.800 o f 0.0 448.0 m 65.8 0 32 (P\2551) W 0 -448.0 m n 1.250 o f 65.8 0 32 (, 2) W n 0.800 o f 0.0 448.0 m 65.8 0 32 (P\2551) W 0 -448.0 m n 1.250 o f 65.8 0 32 (\2551], and input to the Forward DCT \(FDCT\). ) W 300 -11050 M 364.5 0 32 (At the output from the decoder, the Inverse DCT) W 300 -12150 M 551.1 0 32 (\(IDCT\) outputs 8x8 sample blocks to form the) W 300 -13250 M 127.0 0 32 (reconstructed image. The following equations are the) W 300 -14350 M 258.8 0 32 (idealized mathematical definitions of the 8x8 FDCT) W 300 -15450 M (and 8x8 IDCT:) h 300 -24986 M 300 -39590 M 300 -40690 M /Times-Roman-ISOLatin1 F 1000 o f 125.0 0 32 (The DCT is related to the Discrete Fourier Transform) W 300 -41790 M 670.7 0 32 (\(DFT\). Some simple intuition for DCT\255based) W 300 -42890 M 9.1 0 32 (compression can be obtained by viewing the FDCT as a) W 300 -43990 M 496.1 0 32 (harmonic analyzer and the IDCT as a harmonic) W 300 -45090 M 107.6 0 32 (synthesizer. Each 8x8 block of source image samples) W 300 -46190 M 326.3 0 32 (is effectively a 64\255point discrete signal which is a) W 300 -47290 M 174.8 0 32 (function of the two spatial dimensions ) W /Times-Italic-ISOLatin1 $ /Times-Italic & P /Times-Italic-ISOLatin1 F 1000 o f 174.8 0 32 (x ) W /Times-Roman-ISOLatin1 F 1000 o f 174.8 0 32 (and ) W /Times-Italic-ISOLatin1 F 1000 o f 174.8 0 32 (y) W /Times-Roman-ISOLatin1 F 1000 o f 174.8 0 32 (. The) W 300 -48390 M 83.0 0 32 (FDCT takes such a signal as its input and decomposes) W 300 -49490 M 104.6 0 32 (it into 64 orthogonal basis signals. Each contains one) W 300 -50590 M 583.0 0 32 (of the 64 unique two\255dimensional \(2D\) ) W 583.0 0 32 (\026) W 583.0 0 32 (spatial) W 300 -51690 M 683.2 0 32 (frequencies'' which comprise the input signal's) W 300 -52790 M 146.3 0 32 (\026) W 146.3 0 32 (spectrum.) W 146.3 0 32 (\027) W 146.3 0 32 ( The ouput of the FDCT is the set of 64) W 300 -53890 M 227.6 0 32 (basis\255signal amplitudes or ) W 227.6 0 32 (\026) W 227.6 0 32 (DCT coefficients) W 227.6 0 32 (\027) W 227.6 0 32 ( whose) W 300 -54990 M 518.5 0 32 (values are uniquely determined by the particular) W 300 -56090 M (64\255point input signal.) h 300 -57190 M 300 -58290 M 28.0 0 32 (The DCT coefficient values can thus be regarded as the) W 300 -59390 M 43.7 0 32 (relative amount of the 2D spatial frequencies contained) W 300 -60490 M 86.2 0 32 (in the 64\255point input signal. The coefficient with zero) W 300 -61590 M 495.7 0 32 (frequency in both dimensions is called the ) W 495.7 0 32 (\026) W 495.7 0 32 (DC) W 300 -62690 M 435.5 0 32 (coefficient) W 435.5 0 32 (\027) W 435.5 0 32 ( and the remaining 63 coefficients are) W 300 -63790 M 135.1 0 32 (called the ) W 135.1 0 32 (\026) W 135.1 0 32 (AC coefficients.'' Because sample values) W -31919 7200 T S N S 32078 -31436 22722 8436 @ I N 32078 -23000 T N S 10569 -3390 M /Courier-ISOLatin1 $ /Courier & P /Courier-ISOLatin1 F 2400 o f ([) h R N S 201 -5530 20216 5128 @ I N 201 -402 T N N S 0 -5128 20217 5128 @ I N 0 0 T N S 800 -2733 M /Dutch801-Italic-DECmath_Italic F 1200 o f (F) h R S 1533 -2751 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 1933 -2734 M /Dutch801-Italic-DECmath_Italic F 1200 o f (u) h R S 2533 -2751 M /Times-Roman-ISOLatin1 F 1200 o f (,) h R S 3011 -2733 M /Dutch801-Italic-DECmath_Italic F 1200 o f (v) h R S 3544 -2751 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 4477 -2751 M /Times-Roman-ISOLatin1 F 1200 o f (=) h R S 5687 -2251 M /Times-Roman-ISOLatin1 F 1000 o f (1) h R S N 5687.00 -2466.00 M 6187.00 -2466.00 L S 49 w 0 c 0 j 2 i 0.00 G k R R S 5687 -3292 M /Times-Roman-ISOLatin1 F 1000 o f (4) h R S 6187 -2751 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 6487 -2734 M /Dutch801-Italic-DECmath_Italic F 1200 o f (C) h R S 7288 -2751 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 7687 -2734 M /Dutch801-Italic-DECmath_Italic F 1200 o f (u) h R S 8287 -2751 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 8687 -2734 M /Dutch801-Italic-DECmath_Italic F 1200 o f (C) h R S 9487 -2751 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 9887 -2733 M /Dutch801-Italic-DECmath_Italic F 1200 o f (v) h R S 10420 -2655 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 11719 -1159 M /Dutch801-Roman-DECmath_Extension F 1200 o f (X) h R S 12336 -999 M /Times-Roman-ISOLatin1 F 1000 o f (7) h R S 11832 -4208 M /Dutch801-Italic-DECmath_Italic F 1000 o f (x) h R S 12276 -4129 M /Times-Roman-ISOLatin1 F 1000 o f (=0) h R S 13452 -2751 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 13752 -1159 M /Dutch801-Roman-DECmath_Extension F 1200 o f (X) h R S 14369 -999 M /Times-Roman-ISOLatin1 F 1000 o f (7) h R S 13865 -4208 M /Dutch801-Italic-DECmath_Italic F 1000 o f (y) h R S 14309 -4129 M /Times-Roman-ISOLatin1 F 1000 o f (=0) h R S 15485 -2751 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 15785 -2733 M /Dutch801-Italic-DECmath_Italic F 1200 o f (f) h R S 16119 -2751 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 16518 -2734 M /Dutch801-Italic-DECmath_Italic F 1200 o f (x) h R S 17051 -2751 M /Times-Roman-ISOLatin1 F 1200 o f (,) h R S 17529 -2733 M /Dutch801-Italic-DECmath_Italic F 1200 o f (y) h R S 18062 -2751 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 18817 -2752 M /Times-Roman-ISOLatin1 F 1200 o f (*) h R R R N S 4395 -8872 13213 3514 @ I N 4395 -5358 T N N S 0 -3514 13213 3514 @ I N 0 0 T N S 800 -2152 M /Dutch801-Italic-DECmath_Italic F 1200 o f (cos) h R S 2400 -2170 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 2700 -1492 M /Times-Roman-ISOLatin1 F 1000 o f (\(2) h R S 3533 -1571 M /Dutch801-Italic-DECmath_Italic F 1000 o f (x) h R S 3977 -1492 M /Times-Roman-ISOLatin1 F 1000 o f (+1\)) h R S 5374 -1571 M /Dutch801-Italic-DECmath_Italic F 1000 o f (u\271) h R S N 2700.00 -1885.00 M 6485.00 -1885.00 L S 49 w 0 c 0 j 2 i 0.00 G k R R S 4092 -2716 M /Times-Roman-ISOLatin1 F 1000 o f (16) h R S 6485 -2170 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 6785 -2152 M /Dutch801-Italic-DECmath_Italic F 1200 o f (cos) h R S 8384 -2170 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 8684 -1492 M /Times-Roman-ISOLatin1 F 1000 o f (\(2) h R S 9517 -1571 M /Dutch801-Italic-DECmath_Italic F 1000 o f (y) h R S 9961 -1492 M /Times-Roman-ISOLatin1 F 1000 o f (+1\)) h R S 11358 -1571 M /Dutch801-Italic-DECmath_Italic F 1000 o f (v\271) h R S N 8684.00 -1885.00 M 12413.00 -1885.00 L S 49 w 0 c 0 j 2 i 0.00 G k R R S 10049 -2716 M /Times-Roman-ISOLatin1 F 1000 o f (16) h R S 12215 -2349 M /Courier-ISOLatin1 F 2400 o f (]) h R R R S 21404 -7275 M /Times-Roman-ISOLatin1 F 1000 o f (\(1\)) h R R R S N S 31426 -46040 24026 13504 @ I N 31426 -32536 T N S 6588 -3007 M /Courier-ISOLatin1 F 2400 o f ([) h R N S 1158 -4898 19824 4926 @ I N 1158 28 T N N S 0 -4926 19824 4926 @ I N 0 0 T N S 800 -2732 M /Dutch801-Italic-DECmath_Italic F 1200 o f (f) h R S 1134 -2750 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 1533 -2733 M /Dutch801-Italic-DECmath_Italic F 1200 o f (x) h R S 2066 -2750 M /Times-Roman-ISOLatin1 F 1200 o f (,) h R S 2544 -2732 M /Dutch801-Italic-DECmath_Italic F 1200 o f (y) h R S 3077 -2750 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 4010 -2750 M /Times-Roman-ISOLatin1 F 1200 o f (=) h R S 5221 -2154 M /Times-Roman-ISOLatin1 F 1000 o f (1) h R S N 5221.00 -2465.00 M 5721.00 -2465.00 L S 49 w 0 c 0 j 2 i 0.00 G k R R S 5221 -3291 M /Times-Roman-ISOLatin1 F 1000 o f (4) h R S 6621 -1158 M /Dutch801-Roman-DECmath_Extension F 1200 o f (X) h R S 7237 -997 M /Times-Roman-ISOLatin1 F 1000 o f (7) h R S 6705 -4207 M /Dutch801-Italic-DECmath_Italic F 1000 o f (u) h R S 7205 -4128 M /Times-Roman-ISOLatin1 F 1000 o f (=0) h R S 8353 -2750 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 8653 -1158 M /Dutch801-Roman-DECmath_Extension F 1200 o f (X) h R S 9270 -997 M /Times-Roman-ISOLatin1 F 1000 o f (7) h R S 8766 -4207 M /Dutch801-Italic-DECmath_Italic F 1000 o f (v) h R S 9210 -4128 M /Times-Roman-ISOLatin1 F 1000 o f (=0) h R S 10386 -2750 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 10686 -2733 M /Dutch801-Italic-DECmath_Italic F 1200 o f (C) h R S 11487 -2750 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 11886 -2733 M /Dutch801-Italic-DECmath_Italic F 1200 o f (u) h R S 12486 -2750 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 12886 -2733 M /Dutch801-Italic-DECmath_Italic F 1200 o f (C) h R S 13686 -2750 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 14086 -2732 M /Dutch801-Italic-DECmath_Italic F 1200 o f (v) h R S 14619 -2750 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 15018 -2732 M /Dutch801-Italic-DECmath_Italic F 1200 o f (F) h R S 15751 -2750 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 16151 -2733 M /Dutch801-Italic-DECmath_Italic F 1200 o f (u) h R S 16751 -2750 M /Times-Roman-ISOLatin1 F 1200 o f (,) h R S 17229 -2732 M /Dutch801-Italic-DECmath_Italic F 1200 o f (v) h R S 17762 -2750 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 18504 -2820 M /Times-Roman-ISOLatin1 F 1200 o f (*) h R R R N S 4344 -8388 13213 3514 @ I N 4344 -4874 T N N S 0 -3514 13213 3514 @ I N 0 0 T N S 800 -2152 M /Dutch801-Italic-DECmath_Italic F 1200 o f (cos) h R S 2400 -2170 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 2700 -1492 M /Times-Roman-ISOLatin1 F 1000 o f (\(2) h R S 3533 -1571 M /Dutch801-Italic-DECmath_Italic F 1000 o f (x) h R S 3977 -1492 M /Times-Roman-ISOLatin1 F 1000 o f (+1\)) h R S 5374 -1571 M /Dutch801-Italic-DECmath_Italic F 1000 o f (u\271) h R S N 2700.00 -1885.00 M 6485.00 -1885.00 L S 49 w 0 c 0 j 2 i 0.00 G k R R S 4092 -2716 M /Times-Roman-ISOLatin1 F 1000 o f (16) h R S 6485 -2170 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 6785 -2152 M /Dutch801-Italic-DECmath_Italic F 1200 o f (cos) h R S 8384 -2170 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 8684 -1492 M /Times-Roman-ISOLatin1 F 1000 o f (\(2) h R S 9517 -1571 M /Dutch801-Italic-DECmath_Italic F 1000 o f (y) h R S 9961 -1492 M /Times-Roman-ISOLatin1 F 1000 o f (+1\)) h R S 11358 -1571 M /Dutch801-Italic-DECmath_Italic F 1000 o f (v\271) h R S N 8684.00 -1885.00 M 12413.00 -1885.00 L S 49 w 0 c 0 j 2 i 0.00 G k R R S 10049 -2716 M /Times-Roman-ISOLatin1 F 1000 o f (16) h R S 12358 -2295 M /Courier-ISOLatin1 F 2400 o f (]) h R R R S 22310 -7320 M /Times-Roman-ISOLatin1 F 1000 o f (\(2\)) h R S 1028 -10288 M /Times-Roman-ISOLatin1 F 1100 o f (where:) h R S 15506 -10288 M /Times-Roman-ISOLatin1 F 1000 o f (for) h R S 13014 -12923 M /Times-Roman-ISOLatin1 F 1200 o f ( otherwise.) h R N S 4116 -11330 18079 2884 @ I N 4116 -8446 T N N S 0 -2884 16066 2884 @ I N 0 0 T N S 800 -1799 M /Dutch801-Italic-DECmath_Italic F 1200 o f (C) h R S 1600 -1817 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 2000 -1799 M /Dutch801-Italic-DECmath_Italic F 1200 o f (u) h R S 2600 -1817 M /Times-Roman-ISOLatin1 F 1200 o f (\),) h R S 3478 -1817 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 3778 -1799 M /Dutch801-Italic-DECmath_Italic F 1200 o f (C) h R S 4578 -1817 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 4978 -1798 M /Dutch801-Italic-DECmath_Italic F 1200 o f (v) h R S 5510 -1817 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 6731 -1817 M /Times-Roman-ISOLatin1 F 1200 o f (=) h R S 8229 -1817 M /Times-Roman-ISOLatin1 F 1200 o f (1) h R S 8706 -1799 M /Dutch801-Italic-DECmath_Italic F 1200 o f (=) h R S N 10289.00 -829.00 M 10889.00 -829.00 L S 59 w 0 c 0 j 2 i 0.00 G k R R S 10289 -1817 M /Times-Roman-ISOLatin1 F 1200 o f (2) h R S 9182 -834 M /Dutch801-Roman-DECmath_Symbol F 1200 o f (p) h R S 7243 -1817 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 13118 -1703 M /Dutch801-Italic-DECmath_Italic F 1200 o f (u) h R S 13624 -1817 M /Times-Roman-ISOLatin1 F 1200 o f (,) h R R R N S 4383 -13932 8537 2624 @ I N 4383 -11308 T N N S -4122 -2624 13043 2624 @ I N -4122 0 T N S 4189 -1627 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 4789 -1609 M /Dutch801-Italic-DECmath_Italic F 1200 o f (C) h R S 5589 -1627 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 5989 -1610 M /Dutch801-Italic-DECmath_Italic F 1200 o f (u) h R S 6589 -1627 M /Times-Roman-ISOLatin1 F 1200 o f (\),) h R S 7466 -1627 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 7766 -1609 M /Dutch801-Italic-DECmath_Italic F 1200 o f (C) h R S 8566 -1627 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 8966 -1609 M /Dutch801-Italic-DECmath_Italic F 1200 o f (v) h R S 9499 -1627 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 10432 -1627 M /Times-Roman-ISOLatin1 F 1200 o f (=) h R S 11643 -1627 M /Times-Roman-ISOLatin1 F 1200 o f (1) h R R R S 18113 -10213 M /Dutch801-Italic-DECmath_Italic F 1200 o f (v) h R S 18989 -10231 M /Times-Roman-ISOLatin1 F 1200 o f (=) h R S 20581 -10423 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 20703 -10328 M /Times-Roman-ISOLatin1 F 1200 o f (;) h R S 20734 -10327 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 19903 -10231 M /Times-Roman-ISOLatin1 F 1200 o f (0) h R R R R S 30583 -75259 M /Times-Roman-ISOLatin1 F 1000 o f (3) h R showpage $P e %%Page: 4 4 /$P a D g N 0 79200 T S R S 6325 -37291 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 277.4 0 32 (typically vary slowly from point to point across an) W 300 -2150 M 166.3 0 32 (image, the FDCT processing step lays the foundation) W 300 -3250 M 129.5 0 32 (for achieving data compression by concentrating most) W 300 -4350 M 191.6 0 32 (of the signal in the lower spatial frequencies. For a) W 300 -5450 M 93.6 0 32 (typical 8x8 sample block from a typical source image,) W 300 -6550 M 125.4 0 32 (most of the spatial frequencies have zero or near\255zero) W 300 -7650 M (amplitude and need not be encoded.) h 300 -8750 M 300 -9850 M 79.9 0 32 (At the decoder the IDCT reverses this processing step. ) W 300 -10950 M 175.8 0 32 (It takes the 64 DCT coefficients \(which at that point) W 300 -12050 M 43.7 0 32 (have been quantized\) and reconstructs a 64\255point ouput) W 300 -13150 M 855.7 0 32 (image signal by summing the basis signals. ) W 300 -14250 M 254.3 0 32 (Mathematically, the DCT is one\255to\255one mapping for) W 300 -15350 M 107.3 0 32 (64\255point vectors between the image and the frequency) W 300 -16450 M 135.6 0 32 (domains. If the FDCT and IDCT could be computed) W 300 -17550 M 56.0 0 32 (with perfect accuracy and if the DCT coefficients were) W 300 -18650 M 412.3 0 32 (not quantized as in the following description, the) W 300 -19750 M 59.0 0 32 (original 64\255point signal could be exactly recovered. In) W 300 -20850 M 260.1 0 32 (principle, the DCT introduces no loss to the source) W 300 -21950 M 83.0 0 32 (image samples; it merely transforms them to a domain) W 300 -23050 M (in which they can be more efficiently encoded. ) h 300 -24150 M 300 -25250 M 675.7 0 32 (Some properties of practical FDCT and IDCT) W 300 -26350 M 462.7 0 32 (implementations raise the issue of what precisely) W 300 -27450 M 579.6 0 32 (should be required by the JPEG standard. A) W 300 -28550 M 368.7 0 32 (fundamental property is that the FDCT and IDCT) W 300 -29650 M 1721.7 0 32 (equations contain transcendental functions. ) W 300 -30750 M 922.8 0 32 (Consequently, no physical implementation can) W 300 -31850 M 156.5 0 32 (compute them with perfect accuracy. Because of the) W 300 -32950 M 231.0 0 32 (DCT's application importance and its relationship to) W 300 -34050 M 388.6 0 32 (the DFT, many different algorithms by which the) W -6325 37291 T R S 31919 -37291 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 F 1000 o f 11.7 0 32 (FDCT and IDCT may be approximately computed have) W 300 -2150 M 382.1 0 32 (been devised [16]. Indeed, research in fast DCT) W 300 -3250 M 439.7 0 32 (algorithms is ongoing and no single algorithm is) W 300 -4350 M 204.3 0 32 (optimal for all implementations. What is optimal in) W 300 -5450 M 166.6 0 32 (software for a general\255purpose CPU is unlikely to be) W 300 -6550 M 194.3 0 32 (optimal in firmware for a programmable DSP and is) W 300 -7650 M (certain to be suboptimal for dedicated VLSI.) h 300 -8750 M 300 -9850 M 94.1 0 32 (Even in light of the finite precision of the DCT inputs) W 300 -10950 M 228.3 0 32 (and outputs, independently designed implementations) W 300 -12050 M 3.0 0 32 (of the very same FDCT or IDCT algorithm which differ) W 300 -13150 M 62.4 0 32 (even minutely in the precision by which they represent) W 300 -14250 M 55.4 0 32 (cosine terms or intermediate results, or in the way they) W 300 -15350 M 522.8 0 32 (sum and round fractional values, will eventually) W 300 -16450 M (produce slightly different outputs from identical inputs.) h 300 -17550 M 300 -18650 M 101.8 0 32 (To preserve freedom for innovation and customization) W 300 -19750 M 235.5 0 32 (within implementations, JPEG has chosen to specify) W 300 -20850 M 215.0 0 32 (neither a unique FDCT algorithm or a unique IDCT) W 300 -21950 M 491.6 0 32 (algorithm in its proposed standard. This makes) W 300 -23050 M 610.8 0 32 (compliance somewhat more difficult to confirm,) W 300 -24150 M 783.6 0 32 (because two compliant encoders \(or decoders\)) W 300 -25250 M 425.5 0 32 (generally will not produce identical outputs given) W 300 -26350 M 135.0 0 32 (identical inputs. The JPEG standard will address this) W 300 -27450 M 330.2 0 32 (issue by specifying an accuracy test as part of its) W 300 -28550 M 463.0 0 32 (compliance tests for all DCT\255based encoders and) W 300 -29650 M 202.4 0 32 (decoders; this is to ensure against crudely inaccurate) W 300 -30750 M 351.7 0 32 (cosine basis functions which would degrade image) W 300 -31850 M (quality.) h 300 -32950 M -31919 37291 T R S 6807 -5369 T N S 0 -31926 48224 31926 @ R 0 G 300 -1050 M 300 -32454 M S 0 -31926 48224 31926 @ R -6807 5369 T S N S 7334 -36777 47169 30008 @ I N 7334 -6769 T N S 4831 -1639 M /Times-Roman-ISOLatin1 F 952 o f ( ) h n 1.050 o f (8x8 blocks) h n 0.920 o f ( ) h n 1.087 o f (DCT\255Based Encoder) h R S 12324 -4884 M /Times-Roman-ISOLatin1 F 953 o f (FDCT Quantizer) h R S 26405 -4469 M /Times-Roman-ISOLatin1 F 952 o f ( Entropy) h R S 26238 -5384 M /Times-Roman-ISOLatin1 F 953 o f ( Encoder) h R S 4449 -9800 M /Times-Roman-ISOLatin1 F 952 o f ( Source Table Table Compressed) h R S 5855 -3376 M /Symbol F 956 o f (\267) h R S 26371 -10785 M /Times-Roman-ISOLatin1 F 952 o f (Specifications Image Data) h R S 4285 -7317 4498 4499 @ S 75 w 0 c 0 j 2 i 0.00 G k R R S N 5855.00 -2848.00 M 5855.00 -5679.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 7394.00 -3392.00 M 4309.00 -3392.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 7394.00 -3854.00 M 4309.00 -3854.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 7394.00 -4827.00 M 4309.00 -4827.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 6370.00 -2848.00 M 6370.00 -5679.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 5338.00 -2848.00 M 5338.00 -5679.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 4824.00 -2848.00 M 4824.00 -5679.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S 18156 -6304 5249 3497 @ S 75 w 0 c 0 j 2 i 0.00 G k R R S 25572 -6304 5248 3497 @ S 75 w 0 c 0 j 2 i 0.00 G k R R S 10909 -6304 5249 3497 @ S 75 w 0 c 0 j 2 i 0.00 G k R R S N 16116.00 -4556.00 M 18078.00 -4556.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 17594.00 -4810.00 M 18137.00 -4556.00 L 17594.00 -4303.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 23531.00 -4640.00 M 25494.00 -4640.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 25010.00 -4894.00 M 25553.00 -4640.00 L 25010.00 -4387.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S 9866 -7803 22162 5746 @ S 300 w 0 c 0 j 0.875 G k R R S 17928 -10786 M /Times-Roman-ISOLatin1 F 953 o f ( Specifications) h R S 33028 -5389 7722 1583 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S 4730 -10756 M /Times-Roman-ISOLatin1 F 952 o f (Image Data) h R S N 20737.00 -8888.00 M 20737.00 -6505.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 20991.00 -6990.00 M 20737.00 -6446.00 L 20484.00 -6990.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 28486.00 -8960.00 M 28486.00 -6422.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 28740.00 -6907.00 M 28486.00 -6363.00 L 28233.00 -6907.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 8784.00 -4472.00 M 10749.00 -4472.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 10265.00 -4726.00 M 10808.00 -4472.00 L 10265.00 -4219.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 30777.00 -4640.00 M 32977.00 -4640.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 32493.00 -4894.00 M 33036.00 -4640.00 L 32493.00 -4387.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 7394.00 -4368.00 M 4309.00 -4368.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 6145.00 -3100.00 M 7453.00 -1795.00 L S 0.00 G E R S 50 w 0 c 0 j 2 i 0.00 G k R R S 25538 -11119 6457 2163 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S 17583 -11119 6457 2163 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S N 19655.00 -19554.00 M 21722.00 -19554.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 21238.00 -19808.00 M 21781.00 -19554.00 L 21238.00 -19301.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S 21912 -21471 5099 3358 @ S 75 w 0 c 0 j 2 i 0.00 G k R R S 14549 -21470 5098 3358 @ S 75 w 0 c 0 j 2 i 0.00 G k R R S 29357 -21470 5099 3357 @ S 75 w 0 c 0 j 2 i 0.00 G k R R S 12673 -23102 22880 5954 @ S 400 w 0 c 0 j 0.875 G k R R S 15119 -19684 M /Times-Roman-ISOLatin1 F 952 o f ( Entropy) h R S 14875 -20720 M /Times-Roman-ISOLatin1 F 953 o f ( Decoder) h R S 21926 -20023 M /Times-Roman-ISOLatin1 F 952 o f ( Dequantizer IDCT) h R S 20991 -16674 M /Times-Roman-ISOLatin1 F 952 o f (DCT\255Based Decoder) h R S 4785 -20333 7049 1519 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S N 27100.00 -19633.00 M 29169.00 -19633.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 28685.00 -19887.00 M 29228.00 -19633.00 L 28685.00 -19380.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 17599.00 -23877.00 M 17599.00 -21524.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 17852.00 -22009.00 M 17598.00 -21465.00 L 17345.00 -22009.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 12008.00 -19628.00 M 14553.00 -19628.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 14069.00 -19881.00 M 14612.00 -19627.00 L 14068.00 -19374.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S 14441 -24997 M /Times-Roman-ISOLatin1 F 952 o f ( Table Table) h R S 13811 -25878 M /Times-Roman-ISOLatin1 F 952 o f ( Specifications Specifications) h R S 6162 -24918 M /Times-Roman-ISOLatin1 F 953 o f (Compressed) h R S 6322 -25958 M /Times-Roman-ISOLatin1 F 953 o f (Image Data) h R S 35576 -25075 M /Times-Roman-ISOLatin1 F 952 o f ( Reconstructed) h R S 36284 -25957 M /Times-Roman-ISOLatin1 F 952 o f ( Image Data) h R S 36972 -22062 4448 4448 @ S 75 w 0 c 0 j 2 i 0.00 G k R R S N 38525.00 -17644.00 M 38525.00 -20445.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 40045.00 -18105.00 M 36996.00 -18105.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 40045.00 -18615.00 M 36996.00 -18615.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 40045.00 -19554.00 M 36996.00 -19554.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 39033.00 -17644.00 M 39033.00 -20445.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 38015.00 -17644.00 M 38015.00 -20445.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 37506.00 -17644.00 M 37506.00 -20445.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 40045.00 -19021.00 M 36996.00 -19021.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 25797.00 -23877.00 M 25797.00 -21524.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 26050.00 -22009.00 M 25796.00 -21465.00 L 25543.00 -22009.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 34472.00 -19706.00 M 36858.00 -19706.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 36374.00 -19959.00 M 36917.00 -19705.00 L 36373.00 -19452.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 13486.00 -19678.00 M 13486.00 -22359.00 L 24363.00 -22359.00 L 24363.00 -23817.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 24110.00 -23333.00 M 24363.00 -23876.00 L 24617.00 -23333.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 16007.00 -22358.00 M 16007.00 -23817.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 15754.00 -23333.00 M 16007.00 -23876.00 L 16261.00 -23333.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S 22435 -26281 6457 2323 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S 13621 -26281 6455 2323 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S 13684 -13555 M /Times-Roman-ISOLatin1 F 1000 o f (Figure 1. DCT\255Based Encoder Processing Steps) h R S 15889 -28638 M /Times-Roman-ISOLatin1 F 1000 o f (Figure 2. DCT\255Based Decoder Processing Steps) h R R R R S 30679 -75354 M /Times-Roman-ISOLatin1 F 1000 o f (4) h R showpage $P e %%Page: 5 5 /$P a D g N 0 79200 T S R S 6312 -7174 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 325.3 0 32 (For each DCT\255based mode of operation, the JPEG) W 300 -2150 M 12.0 0 32 (proposal specifies separate codecs for images with 8\255bit) W 300 -3250 M 17.4 0 32 (and 12\255bit \(per component\) source image samples. The) W 300 -4350 M 71.6 0 32 (12\255bit codecs, needed to accommodate certain types of) W 300 -5450 M 1166.8 0 32 (medical and other images, require greater) W 300 -6550 M 83.3 0 32 (computational resources to achieve the required FDCT) W 300 -7650 M 595.3 0 32 (or IDCT accuracy. Images with other sample) W 300 -8750 M 162.7 0 32 (precisions can usually be accommodated by either an) W 300 -9850 M 58.0 0 32 (8\255bit or 12\255bit codec, but this must be done outside the) W 300 -10950 M 534.4 0 32 (JPEG standard. For example, it would be the) W 300 -12050 M 101.6 0 32 (responsibility of an application to decide how to fit or) W 300 -13150 M 402.5 0 32 (pad a 6\255bit sample into the 8\255bit encoder's input) W 300 -14250 M 46.3 0 32 (interface, how to unpack it at the decoder's output, and) W 300 -15350 M (how to encode any necessary related information.) h 300 -16450 M 300 -17550 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1000 o f (4.2 Quantization) h 300 -19250 M /Times-Roman-ISOLatin1 F 1000 o f 296.1 0 32 (After output from the FDCT, each of the 64 DCT) W 300 -20350 M 73.7 0 32 (coefficients is uniformly quantized in conjunction with) W 300 -21450 M 495.2 0 32 (a 64\255element Quantization Table, which must be) W 300 -22550 M 66.6 0 32 (specified by the application \(or user\) as an input to the) W 300 -23650 M 19.7 0 32 (encoder. Each element can be any integer value from 1) W 300 -24750 M 13.9 0 32 (to 255, which specifies the step size of the quantizer for) W 300 -25850 M 277.7 0 32 (its corresponding DCT coefficient. The purpose of) W 300 -26950 M 453.5 0 32 (quantization is to achieve further compression by) W 300 -28050 M 18.7 0 32 (representing DCT coefficients with no greater precision) W 300 -29150 M 93.8 0 32 (than is necessary to achieve the desired image quality. ) W 300 -30250 M 110.9 0 32 (Stated another way, the goal of this processing step is) W 300 -31350 M 39.1 0 32 (to discard information which is not visually significant.) W 300 -32450 M 125.0 0 32 (Quantization is a many\255to\255one mapping, and therefore) W 300 -33550 M 215.8 0 32 (is fundamentally lossy. It is the principal source of) W 300 -34650 M (lossiness in DCT\255based encoders.) h 300 -35750 M 300 -36850 M 448.1 0 32 (Quantization is defined as division of each DCT) W 300 -37950 M 310.2 0 32 (coefficient by its corresponding quantizer step size,) W 300 -39050 M (followed by rounding to the nearest integer:) h 300 -40150 M -6312 7174 T S N S 6806 -52373 22051 4699 @ I N 6806 -47674 T N N S 1946 -4021 18495 3678 @ I N 1946 -343 T N N S 0 -3199 18495 3199 @ I N 0 0 T N S 800 -2152 M /Dutch801-Italic-DECmath_Italic F 1200 o f (F) h R S 1533 -1492 M /Dutch801-Italic-DECmath_Italic F 800 o f (Q) h R S 2111 -2170 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 2510 -2152 M /Dutch801-Italic-DECmath_Italic F 1200 o f (u) h R S 3110 -2170 M /Times-Roman-ISOLatin1 F 1200 o f (,) h R S 3588 -2151 M /Dutch801-Italic-DECmath_Italic F 1200 o f (v) h R S 4121 -2170 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 4521 -2170 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 5354 -2170 M /Times-Roman-ISOLatin1 F 1200 o f (=) h R S 6565 -2170 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 6865 -2152 M /Dutch801-Italic-DECmath_Italic F 1200 o f (Integer) h R S 10331 -2170 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 10631 -2152 M /Dutch801-Italic-DECmath_Italic F 1200 o f (Round) h R S 13764 -2170 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 14064 -2170 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 14519 -1492 M /Times-Roman-ISOLatin1 F 1000 o f ( ) h R S 14769 -1571 M /Dutch801-Italic-DECmath_Italic F 1000 o f (F) h R S 15380 -1492 M /Times-Roman-ISOLatin1 F 1000 o f (\() h R S 15713 -1571 M /Dutch801-Italic-DECmath_Italic F 1000 o f (u) h R S 16213 -1492 M /Times-Roman-ISOLatin1 F 1000 o f (,) h R S 16463 -1571 M /Dutch801-Italic-DECmath_Italic F 1000 o f (v) h R S 16907 -1492 M /Times-Roman-ISOLatin1 F 1000 o f (\)) h R S 14463 -2789 M /Dutch801-Italic-DECmath_Italic F 1000 o f (Q) h R S 15185 -2710 M /Times-Roman-ISOLatin1 F 1000 o f (\() h R S 15518 -2789 M /Dutch801-Italic-DECmath_Italic F 1000 o f (u) h R S 16018 -2710 M /Times-Roman-ISOLatin1 F 1000 o f (,) h R S 16268 -2789 M /Dutch801-Italic-DECmath_Italic F 1000 o f (v) h R S 16712 -2710 M /Times-Roman-ISOLatin1 F 1000 o f (\)) h R S N 14463.00 -1885.00 M 17295.00 -1885.00 L S 49 w 0 c 0 j 2 i 0.00 G k R R S 17045 -2710 M /Times-Roman-ISOLatin1 F 1000 o f ( ) h R S 17295 -2170 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R R R S 20876 -2965 M /Times-Roman-ISOLatin1 F 1000 o f (\(3\)) h R R R R S 31919 -7170 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 F 1000 o f 152.5 0 32 (This output value is normalized by the quantizer step) W 300 -2150 M 117.9 0 32 (size. Dequantization is the inverse function, which in) W 300 -3250 M 471.7 0 32 (this case means simply that the normalization is) W 300 -4350 M 51.8 0 32 (removed by multiplying by the step size, which returns) W 300 -5450 M 9.2 0 32 (the result to a representation appropriate for input to the) W 300 -6550 M (IDCT:) h 300 -11965 M /Times-Roman-ISOLatin1 F 1000 o f 205.4 0 32 (When the aim is to compress the image as much as) W 300 -13065 M 71.1 0 32 (possible without visible artifacts, each step size ideally) W 300 -14165 M 173.5 0 32 (should be chosen as the perceptual threshold or ) W 173.5 0 32 (\026) W 173.5 0 32 (just) W 300 -15265 M 91.3 0 32 (noticeable difference) W 91.3 0 32 (\027) W 91.3 0 32 ( for the visual contribution of its) W 300 -16365 M 97.0 0 32 (corresponding cosine basis function. These thresholds) W 300 -17465 M 151.0 0 32 (are also functions of the source image characteristics,) W 300 -18565 M 458.2 0 32 (display characteristics and viewing distance. For) W 300 -19665 M 43.7 0 32 (applications in which these variables can be reasonably) W 300 -20765 M 755.4 0 32 (well defined, psychovisual experiments can be) W 300 -21865 M 428.4 0 32 (performed to determine the best thresholds. The) W 300 -22965 M 410.4 0 32 (experiment described in [12] has led to a set of) W 300 -24065 M 388.7 0 32 (Quantization Tables for CCIR\255601 [4] images and) W 300 -25165 M 309.4 0 32 (displays. These have been used experimentally by) W 300 -26265 M 5.5 0 32 (JPEG members and will appear in the ISO standard as a) W 300 -27365 M (matter of information, but not as a requirement.) h 300 -28465 M 300 -29565 M /Times-Bold-ISOLatin1 F 1000 o f (4.3 DC Coding and Zig\255Zag Sequence) h 300 -31265 M /Times-Roman-ISOLatin1 F 1000 o f 560.2 0 32 (After quantization, the DC coefficient is treated) W 300 -32365 M 371.5 0 32 (separately from the 63 AC coefficients. The DC) W 300 -33465 M 83.6 0 32 (coefficient is a measure of the average value of the 64) W 300 -34565 M 483.9 0 32 (image samples. Because there is usually strong) W 300 -35665 M 12.1 0 32 (correlation between the DC coefficients of adjacent 8x8) W 300 -36765 M 93.8 0 32 (blocks, the quantized DC coefficient is encoded as the) W 300 -37865 M 138.9 0 32 (difference from the DC term of the previous block in) W 300 -38965 M 24.3 0 32 (the encoding order \(defined in the following\), as shown) W 300 -40065 M 157.1 0 32 (in Figure 3. This special treatment is worthwhile, as) W 300 -41165 M 9.3 0 32 (DC coefficients frequently contain a significant fraction) W 300 -42265 M (of the total image energy.) h 300 -43365 M -31919 7170 T S N S 32270 -18385 22338 4315 @ I N 32270 -14070 T N N S 3092 -3422 16296 3021 @ I N 3092 -401 T N N S 0 -3021 16296 3021 @ I N 0 0 T N S 800 -1999 M /Dutch801-Italic-DECmath_Italic F 1200 o f (F) h R S 1533 -1339 M /Dutch801-Italic-DECmath_Italic F 800 o f (Q) h R S 2236 -1250 M /Dutch801-Roman-DECmath_Symbol F 695 o f (0) h R S 2333 -2017 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 2733 -1999 M /Dutch801-Italic-DECmath_Italic F 1200 o f (u) h R S 3333 -2016 M /Times-Roman-ISOLatin1 F 1200 o f (,) h R S 3811 -1998 M /Dutch801-Italic-DECmath_Italic F 1200 o f (v) h R S 4344 -2016 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 4743 -2017 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 5577 -2017 M /Times-Roman-ISOLatin1 F 1200 o f (=) h R S 6787 -1999 M /Dutch801-Italic-DECmath_Italic F 1200 o f (F) h R S 7521 -1339 M /Dutch801-Italic-DECmath_Italic F 800 o f (Q) h R S 8098 -2016 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 8498 -1999 M /Dutch801-Italic-DECmath_Italic F 1200 o f (u) h R S 9098 -2016 M /Times-Roman-ISOLatin1 F 1200 o f (,) h R S 9576 -1998 M /Dutch801-Italic-DECmath_Italic F 1200 o f (v) h R S 10108 -2016 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 12219 -1999 M /Dutch801-Italic-DECmath_Italic F 1200 o f (Q) h R S 13086 -2016 M /Times-Roman-ISOLatin1 F 1200 o f (\() h R S 13485 -1999 M /Dutch801-Italic-DECmath_Italic F 1200 o f (u) h R S 14085 -2016 M /Times-Roman-ISOLatin1 F 1200 o f (,) h R S 14563 -1998 M /Dutch801-Italic-DECmath_Italic F 1200 o f (v) h R S 15096 -2016 M /Times-Roman-ISOLatin1 F 1200 o f (\)) h R S 11136 -2333 M /Times-Roman-ISOLatin1 F 1000 o f (*) h R R R S 20916 -2456 M /Times-Roman-ISOLatin1 F 1000 o f (\(4\)) h R R R R S 6328 -51770 T N S 0 -19270 48703 19270 @ R 0 G 300 -1050 M 300 -18936 M S 0 -19270 48703 19270 @ R -6328 51770 T S N S 6759 -69660 47840 16490 @ I N 6759 -53170 T N S N 24946.00 -873.00 M 26265.00 -2033.00 L S 40 w 0 c 0 j 2 i 0.00 G k R R S N 25725.00 -1896.00 M 26301.00 -2065.00 L 26060.00 -1516.00 L S 40 w 0 c 0 j 2 i 0.00 G k R R S N 38584.00 -11977.00 M 37539.00 -11120.00 L S 40 w 0 c 0 j 2 i 0.00 G k R R S N 38083.00 -11238.00 M 37502.00 -11089.00 L 37761.00 -11630.00 L S 40 w 0 c 0 j 2 i 0.00 G k R R S N 27031.00 -874.00 M 28353.00 -2033.00 L S 40 w 0 c 0 j 2 i 0.00 G k R R S N 27813.00 -1897.00 M 28389.00 -2065.00 L 28147.00 -1516.00 L S 40 w 0 c 0 j 2 i 0.00 G k R R S 18189 -6843 M /Times-Roman-ISOLatin1 F 974 o f (. . .) h R S 9345 -10125 M /Times-Roman-ISOLatin1 F 973 o f (DIFF) h 0.0 -436.0 m ( ) h 0 436.0 m (= DC) h n 0.801 o f 0.0 -349.0 m (i) h 0 349.0 m n 1.249 o f 0.0 -436.0 m ( ) h 0 436.0 m (\255 DC) h n 0.801 o f 0.0 -349.0 m (i\2551) h 0 349.0 m R S 10936 -3013 M /Times-Roman-ISOLatin1 F 973 o f ( DC) h n 0.801 o f 0.0 -349.0 m (i\2551) h 0 349.0 m n 1.249 o f ( DC) h n 0.801 o f 0.0 -349.0 m (i) h 0 349.0 m R S N 11470.00 -3233.00 M 10035.00 -4378.00 L S 0.00 G E R S 40 w 0 c 0 j 2 i 0.00 G k R R S N 10264.00 -3871.00 M 9997.00 -4408.00 L 10580.00 -4267.00 L S 40 w 0 c 0 j 2 i 0.00 G k R R S N 16221.00 -3158.00 M 14612.00 -4168.00 L S 0.00 G E R S 40 w 0 c 0 j 2 i 0.00 G k R R S N 14897.00 -3690.00 M 14571.00 -4193.00 L 15166.00 -4119.00 L S 40 w 0 c 0 j 2 i 0.00 G k R R S 26789 -2756 M /Symbol F 973 o f (\267) h R S 28180 -2673 M /Symbol F 975 o f (\267) h R S 29672 -2673 M /Symbol F 973 o f (\267) h R S 31162 -2673 M /Symbol F 973 o f (\267) h R S 32652 -2673 M /Symbol F 975 o f (\267) h R S 34241 -2673 M /Symbol F 975 o f (\267) h R S 35533 -2673 M /Symbol F 975 o f (\267) h R S 37024 -2673 M /Symbol F 975 o f (\267) h R S 26789 -3895 M /Symbol F 973 o f (\267) h R S 28281 -3895 M /Symbol F 973 o f (\267) h R S 29672 -3895 M /Symbol F 973 o f (\267) h R S 31162 -3895 M /Symbol F 973 o f (\267) h R S 32652 -3895 M /Symbol F 975 o f (\267) h R S 34241 -3895 M /Symbol F 975 o f (\267) h R S 35533 -3895 M /Symbol F 975 o f (\267) h R S 37024 -3895 M /Symbol F 975 o f (\267) h R S 26789 -5036 M /Symbol F 973 o f (\267) h R S 28281 -5036 M /Symbol F 973 o f (\267) h R S 29672 -5036 M /Symbol F 973 o f (\267) h R S 31162 -5036 M /Symbol F 973 o f (\267) h R S 32652 -5036 M /Symbol F 975 o f (\267) h R S 34241 -5036 M /Symbol F 975 o f (\267) h R S 35533 -5036 M /Symbol F 975 o f (\267) h R S 37024 -5036 M /Symbol F 975 o f (\267) h R S 26789 -6178 M /Symbol F 973 o f (\267) h R S 28281 -6178 M /Symbol F 973 o f (\267) h R S 29672 -6178 M /Symbol F 973 o f (\267) h R S 31162 -6178 M /Symbol F 973 o f (\267) h R S 32652 -6178 M /Symbol F 975 o f (\267) h R S 34241 -6178 M /Symbol F 975 o f (\267) h R S 35533 -6178 M /Symbol F 975 o f (\267) h R S 37024 -6178 M /Symbol F 975 o f (\267) h R S 26789 -7483 M /Symbol F 973 o f (\267) h R S 28281 -7483 M /Symbol F 973 o f (\267) h R S 29672 -7483 M /Symbol F 973 o f (\267) h R S 31162 -7483 M /Symbol F 973 o f (\267) h R S 32652 -7483 M /Symbol F 975 o f (\267) h R S 34241 -7483 M /Symbol F 975 o f (\267) h R S 35533 -7483 M /Symbol F 975 o f (\267) h R S 37024 -7483 M /Symbol F 975 o f (\267) h R S 26789 -8703 M /Symbol F 973 o f (\267) h R S 28281 -8703 M /Symbol F 973 o f (\267) h R S 29672 -8703 M /Symbol F 973 o f (\267) h R S 31162 -8703 M /Symbol F 973 o f (\267) h R S 32652 -8703 M /Symbol F 975 o f (\267) h R S 34241 -8703 M /Symbol F 975 o f (\267) h R S 35632 -8624 M /Symbol F 975 o f (\267) h R S 37024 -8703 M /Symbol F 975 o f (\267) h R S 26789 -9845 M /Symbol F 973 o f (\267) h R S 28281 -9845 M /Symbol F 973 o f (\267) h R S 29672 -9845 M /Symbol F 973 o f (\267) h R S 31162 -9845 M /Symbol F 973 o f (\267) h R S 32652 -9845 M /Symbol F 975 o f (\267) h R S 34241 -9845 M /Symbol F 975 o f (\267) h R S 35533 -9845 M /Symbol F 975 o f (\267) h R S 37024 -9845 M /Symbol F 975 o f (\267) h R S 26789 -11069 M /Symbol F 973 o f (\267) h R S 28281 -11069 M /Symbol F 973 o f (\267) h R S 29672 -11069 M /Symbol F 973 o f (\267) h R S 31162 -11069 M /Symbol F 973 o f (\267) h R S 32652 -11069 M /Symbol F 975 o f (\267) h R S 34241 -11069 M /Symbol F 975 o f (\267) h R S 35533 -11069 M /Symbol F 975 o f (\267) h R S 37024 -11069 M /Symbol F 975 o f (\267) h R S 9641 -7946 3957 3243 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S 9668 -5108 465 380 @ S 0.00 G E R S 50 w 0 c 0 j 2 i 0.00 G k R R S 8783 -14166 M /Times-Roman-ISOLatin1 F 1000 o f (Differential DC encoding) h ( ) h (Zig-zag sequence) h R S 9891 -6682 M /Times-Roman-ISOLatin1 F 973 o f (block) h n 0.801 o f 0.0 -349.0 m (i\2551) h 0 349.0 m R S 13963 -6683 M /Times-Roman-ISOLatin1 F 973 o f (block) h n 0.801 o f 0.0 -349.0 m (i) h 0 349.0 m R S 7064 -6843 M /Times-Roman-ISOLatin1 F 974 o f (. . .) h R S N 28400.00 -2444.00 M 27055.00 -3545.00 L 27055.00 -4726.00 L 29918.00 -2378.00 L 31279.00 -2378.00 L 27043.00 -5851.00 L 27043.00 -7171.00 L 32894.00 -2371.00 L 34260.00 -2371.00 L 27010.00 -8316.00 L 27010.00 -9535.00 L 35709.00 -2398.00 L 37151.00 -2398.00 L 26927.00 -10781.00 L 28401.00 -10781.00 L 37212.00 -3555.00 L 37212.00 -4808.00 L 29924.00 -10783.00 L 31282.00 -10783.00 L 37271.00 -5871.00 L 37271.00 -7171.00 L 32878.00 -10769.00 L 34260.00 -10769.00 L 37202.00 -8356.00 L 37202.00 -9535.00 L 35679.00 -10781.00 L 37242.00 -10781.00 L S 40 w 0 c 0 j 2 i 0.00 G k R R S N 34565.00 -9916.00 M 35359.00 -9916.00 L 35359.00 -10488.00 L S 40 w 0 c 0 j 2 i 0.00 G k R R S N 28584.00 -2829.00 M 29377.00 -2829.00 L 29377.00 -3400.00 L S 40 w 0 c 0 j 2 i 0.00 G k R R S N 36352.00 -9592.00 M 36352.00 -10161.00 L 37047.00 -10161.00 L S 40 w 0 c 0 j 2 i 0.00 G k R R S N 27590.00 -2584.00 M 27590.00 -3154.00 L 28286.00 -3154.00 L S 40 w 0 c 0 j 2 i 0.00 G k R R S 24000 -783 M /Times-Roman-ISOLatin1 F 973 o f (DC AC) h n 0.801 o f 0.0 -349.0 m (01) h 0 349.0 m R S 38456 -12854 M /Times-Roman-ISOLatin1 F 974 o f (AC) h n 0.800 o f 0.0 -349.0 m (77) h 0 349.0 m R S N 26839.00 -2400.00 M 28111.00 -2400.00 L S 0.00 G E R S 75 w 0 c 0 j 2 i 0.00 G k R R S N 27656.00 -2654.00 M 28200.00 -2400.00 L 27656.00 -2147.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 35577 -834 M /Times-Roman-ISOLatin1 F 974 o f ( AC) h n 0.800 o f 0.0 -349.0 m (07) h 0 349.0 m R S N 38222.00 -1303.00 M 37504.00 -2055.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 37635.00 -1551.00 M 37442.00 -2119.00 L 38001.00 -1901.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 24060 -12907 M /Times-Roman-ISOLatin1 F 974 o f (AC) h n 0.800 o f 0.0 -349.0 m (70) h 0 349.0 m R S N 25766.00 -12186.00 M 26645.00 -11189.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 26534.00 -11698.00 M 26704.00 -11123.00 L 26154.00 -11363.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 13603 -7946 3956 3243 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S 13630 -5108 463 380 @ S 0.00 G E R S 50 w 0 c 0 j 2 i 0.00 G k R R S 11935 -16293 M /Times-Roman-ISOLatin1 F 1000 o f (Figure 3. Preparation of Quantized Coefficients for Entropy Coding) h R R R R S 30583 -75546 M /Times-Roman-ISOLatin1 F 1000 o f (5) h R showpage $P e %%Page: 6 6 /$P a D g N 0 79200 T S R S 6320 -7197 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 246.1 0 32 (Finally, all of the quantized coefficients are ordered) W 300 -2150 M 194.4 0 32 (into the ) W 194.4 0 32 (\026) W 194.4 0 32 (zig\255zag) W 194.4 0 32 (\027) W 194.4 0 32 ( sequence, also shown in Figure 3. ) W 300 -3250 M 337.0 0 32 (This ordering helps to facilitate entropy coding by) W 300 -4350 M 339.4 0 32 (placing low\255frequency coefficients \(which are more) W 300 -5450 M 994.6 0 32 (likely to be nonzero\) before high\255frequency) W 300 -6550 M (coefficients.) h 300 -7650 M 300 -8750 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1000 o f (4.4 Entropy Coding) h 300 -10450 M /Times-Roman-ISOLatin1 F 1000 o f 537.0 0 32 (The final DCT\255based encoder processing step is) W 300 -11550 M 680.2 0 32 (entropy coding. This step achieves additional) W 300 -12650 M 45.8 0 32 (compression losslessly by encoding the quantized DCT) W 300 -13750 M 194.3 0 32 (coefficients more compactly based on their statistical) W 300 -14850 M 449.0 0 32 (characteristics. The JPEG proposal specifies two) W 300 -15950 M 321.3 0 32 (entropy coding methods \255 Huffman coding [8] and) W 300 -17050 M 87.3 0 32 (arithmetic coding [15]. The Baseline sequential codec) W 300 -18150 M 206.0 0 32 (uses Huffman coding, but codecs with both methods) W 300 -19250 M (are specified for all modes of operation.) h 300 -20350 M 300 -21450 M 311.6 0 32 (It is useful to consider entropy coding as a 2\255step) W 300 -22550 M 12.6 0 32 (process. The first step converts the zig\255zag sequence of) W 300 -23650 M 65.0 0 32 (quantized coefficients into an intermediate sequence of) W 300 -24750 M 166.3 0 32 (symbols. The second step converts the symbols to a) W 300 -25850 M 360.9 0 32 (data stream in which the symbols no longer have) W 300 -26950 M 467.5 0 32 (externally identifiable boundaries. The form and) W 300 -28050 M 90.9 0 32 (definition of the intermediate symbols is dependent on) W 300 -29150 M 34.6 0 32 (both the DCT\255based mode of operation and the entropy) W 300 -30250 M (coding method.) h 300 -31350 M 300 -32450 M 340.3 0 32 (Huffman coding requires that one or more sets of) W 300 -33550 M 198.4 0 32 (Huffman code tables be specified by the application. ) W 300 -34650 M 46.4 0 32 (The same tables used to compress an image are needed) W 300 -35750 M 156.3 0 32 (to decompress it. Huffman tables may be predefined) W 300 -36850 M 24.1 0 32 (and used within an application as defaults, or computed) W 300 -37950 M 821.1 0 32 (specifically for a given image in an initial) W 300 -39050 M 272.7 0 32 (statistics\255gathering pass prior to compression. Such) W 300 -40150 M 118.0 0 32 (choices are the business of the applications which use) W 300 -41250 M 601.5 0 32 (JPEG; the JPEG proposal specifies no required) W 300 -42350 M 333.3 0 32 (Huffman tables. Huffman coding for the Baseline) W 300 -43450 M (sequential encoder is described in detail in section 7.) h 300 -44550 M 300 -45650 M 254.3 0 32 (By contrast, the particular arithmetic coding method) W 300 -46750 M 40.0 0 32 (specified in the JPEG proposal [2] requires no tables to) W 300 -47850 M 169.3 0 32 (be externally input, because it is able to adapt to the) W 300 -48950 M 182.0 0 32 (image statistics as it encodes the image. \(If desired,) W 300 -50050 M 83.0 0 32 (statistical conditioning tables can be used as inputs for) W 300 -51150 M 368.7 0 32 (slightly better efficiency, but this is not required.\) ) W 300 -52250 M 827.6 0 32 (Arithmetic coding has produced 5\25510% better) W 300 -53350 M 289.6 0 32 (compression than Huffman for many of the images) W 300 -54450 M 7.0 0 32 (which JPEG members have tested. However, some feel) W 300 -55550 M 222.1 0 32 (it is more complex than Huffman coding for certain) W 300 -56650 M 749.5 0 32 (implementations, for example, the highest\255speed) W 300 -57750 M 687.0 0 32 (hardware implementations. \(Throughout JPEG's) W 300 -58850 M 72.6 0 32 (history, ) W 72.6 0 32 (\026) W 72.6 0 32 (complexity) W 72.6 0 32 (\027) W 72.6 0 32 ( has proved to be most elusive as) W 300 -59950 M (a practical metric for comparing compression methods.\)) h 300 -61050 M 300 -62150 M 83.4 0 32 (If the only difference between two JPEG codecs is the) W 300 -63250 M 39.4 0 32 (entropy coding method, transcoding between the two is) W -6320 7197 T R S 31919 -7197 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 F 1000 o f 106.6 0 32 (possible by simply entropy decoding with one method) W 300 -2150 M (and entropy recoding with the other.) h 300 -3250 M 300 -4350 M /Times-Bold-ISOLatin1 F 1000 o f (4.5 Compression and Picture Quality) h 300 -6050 M /Times-Roman-ISOLatin1 F 1000 o f 118.9 0 32 (For color images with moderately complex scenes, all) W 300 -7150 M 194.3 0 32 (DCT\255based modes of operation typically produce the) W 300 -8250 M 289.4 0 32 (following levels of picture quality for the indicated) W 300 -9350 M 441.0 0 32 (ranges of compression. These levels are only a) W 300 -10450 M 740.5 0 32 (guideline \255 quality and compression can vary) W 300 -11550 M 139.0 0 32 (significantly according to source image characteristics) W 300 -12650 M 156.3 0 32 (and scene content. \(The units ) W 156.3 0 32 (\026) W 156.3 0 32 (bits/pixel) W 156.3 0 32 (\027) W 156.3 0 32 ( here mean) W 300 -13750 M 262.1 0 32 (the total number of bits in the compressed image \255) W 300 -14850 M 19.6 0 32 (including the chrominance components \255 divided by the) W 300 -15950 M (number of samples in the luminance component.\)) h 300 -17050 M 300 -18150 M /Symbol F 1000 o f (\267) h 2100 -18150 M /Times-Roman-ISOLatin1 F 1000 o f 505.8 0 32 (0.25\2550.5 bits/pixel: moderate to good quality,) W 2100 -19250 M (sufficient for some applications;) h 2100 -20350 M 300 -21450 M /Symbol F 1000 o f (\267) h 2100 -21450 M /Times-Roman-ISOLatin1 F 1000 o f 370.5 0 32 (0.5\2550.75 bits/pixel: good to very good quality,) W 2100 -22550 M (sufficient for many applications;) h 2100 -23650 M 300 -24750 M /Symbol F 1000 o f (\267) h 2100 -24750 M /Times-Roman-ISOLatin1 F 1000 o f 89.4 0 32 (0.75\2551/5 bits/pixel: excellent quality, sufficient for) W 2100 -25850 M (most applications;) h 2100 -26950 M 300 -28050 M /Symbol F 1000 o f (\267) h 2100 -28050 M /Times-Roman-ISOLatin1 F 1000 o f 284.8 0 32 (1.5\2552.0 bits/pixel: usually indistinguishable from) W 2100 -29150 M 333.8 0 32 (the original, sufficient for the most demanding) W 2100 -30250 M (applications.) h 300 -31350 M 300 -32450 M 300 -33700 M /Times-Bold-ISOLatin1 F 1200 o f 162.7 0 32 (5 Processing Steps for Predictive Lossless) W 300 -35000 M (Coding) h 300 -36750 M /Times-Roman-ISOLatin1 F 1000 o f 239.4 0 32 (After its selection of a DCT\255based method in 1988,) W 300 -37850 M 99.0 0 32 (JPEG discovered that a DCT\255based lossless mode was) W 300 -38950 M 69.5 0 32 (difficult to define as a practical standard against which) W 300 -40050 M 761.2 0 32 (encoders and decoders could be independently) W 300 -41150 M 366.2 0 32 (implemented, without placing severe constraints on) W 300 -42250 M (both encoder and decoder implementations.) h 300 -43350 M 300 -44450 M 160.2 0 32 (JPEG, to meet its requirement for a lossless mode of) W 300 -45550 M 448.8 0 32 (operation, has chosen a simple predictive method) W 300 -46650 M 225.9 0 32 (which is wholly independent of the DCT processing) W 300 -47750 M 37.9 0 32 (described previously. Selection of this method was not) W 300 -48850 M 41.5 0 32 (the result of rigorous competitive evaluation as was the) W 300 -49950 M 184.8 0 32 (DCT\255based method. Nevertheless, the JPEG lossless) W 300 -51050 M 626.4 0 32 (method produces results which, in light of its) W 300 -52150 M 104.7 0 32 (simplicity, are surprisingly close to the state of the art) W 300 -53250 M 144.0 0 32 (for lossless continuous\255tone compression, as indicated) W 300 -54350 M (by a recent technical report [5].) h 300 -55450 M 300 -56550 M 465.0 0 32 (Figure 4 shows the main processing steps for a) W 300 -57650 M 282.2 0 32 (single\255component image. A predictor combines the) W 300 -58750 M 5.4 0 32 (values of up to three neighboring samples \(A, B, and C\)) W 300 -59850 M 166.5 0 32 (to form a prediction of the sample indicated by X in) W 300 -60950 M 147.9 0 32 (Figure 5. This prediction is then subtracted from the) W 300 -62050 M 31.1 0 32 (actual value of sample X, and the difference is encoded) W -31919 7197 T R S 30871 -75643 M /Times-Roman-ISOLatin1 F 1000 o f (6) h R showpage $P e %%Page: 7 7 /$P a D g N 0 79200 T S R S 6300 -26613 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 221.9 0 32 (losslessly by either of the entropy coding methods \255) W 300 -2150 M 24.7 0 32 (Huffman or arithmetic. Any one of the eight predictors ) W 300 -3250 M (listed in Table 1 \(under ) h (\026) h (selection\255value) h (\027) h (\) can be used.) h 300 -4350 M 300 -5450 M 178.4 0 32 (Selections 1, 2, and 3 are one\255dimensional predictors) W 300 -6550 M 395.6 0 32 (and selections 4, 5, 6 and 7 are two\255dimensional) W 300 -7650 M 295.1 0 32 (predictors. Selection\255value 0 can only be used for) W 300 -8750 M 666.7 0 32 (differential coding in the hierarchical mode of) W 300 -9850 M 211.6 0 32 (operation. The entropy coding is nearly identical to) W 300 -10950 M 58.7 0 32 (that used for the DC coefficient as described in section) W 300 -12050 M (7.1 \(for Huffman coding\).) h 300 -13150 M 300 -25655 M /Times-Roman-ISOLatin1 F 1000 o f 3.4 0 32 (For the lossless mode of operation, two different codecs) W 300 -26755 M 225.9 0 32 (are specified \255 one for each entropy coding method. ) W 300 -27855 M 62.8 0 32 (The encoders can use any source image precision from) W 300 -28955 M 119.3 0 32 (2 to 16 bits/sample, and can use any of the predictors) W 300 -30055 M 222.3 0 32 (except selection\255value 0. The decoders must handle) W 300 -31155 M 67.9 0 32 (any of the sample precisions and any of the predictors. ) W 300 -32255 M 860.8 0 32 (Lossless codecs typically produce around 2:1) W 300 -33355 M 18.3 0 32 (compression for color images with moderately complex) W 300 -34455 M (scenes.) h -6300 26613 T S N S 6363 -51518 22914 11405 @ I N 6363 -40113 T N S N 8451.00 -362.00 M 8451.00 -7298.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 6930.00 -1720.00 M 15682.00 -1720.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 6930.00 -3077.00 M 15682.00 -3077.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 6930.00 -364.00 M 15682.00 -364.00 L S 100 w 0 c 0 j 2 i 0.00 G k R R S N 6930.00 -5941.00 M 15682.00 -5941.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 10260.00 -362.00 M 10260.00 -7298.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 12069.00 -362.00 M 12069.00 -7298.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 13877.00 -362.00 M 13877.00 -7298.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 6930.00 -4585.00 M 15682.00 -4585.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 6930.00 -362.00 M 6930.00 -7298.00 L S 100 w 0 c 0 j 2 i 0.00 G k R R S 2274 -9820 M /Times-Roman-ISOLatin1 F 1000 o f (Figure 5. 3\255Sample Prediction Neighborhood) h R S 8921 -3989 M /Times-Roman-ISOLatin1 F 1000 o f (C B) h R S 8826 -6038 M /Times-Roman-ISOLatin1 F 1000 o f 0.0 448.0 m (A X) h 0 -448.0 m R R R R S 31919 -25472 T N 0 G 300 -1050 M 300 -17589 M 300 -18839 M 300 -20739 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1200 o f (6 Multiple\255Component Images) h 300 -22489 M /Times-Roman-ISOLatin1 F 1000 o f 323.8 0 32 (The previous sections discussed the key processing) W 300 -23589 M 115.0 0 32 (steps of the DCT\255based and predictive lossless codecs) W 300 -24689 M 31.4 0 32 (for the case of single\255component source images. These) W 300 -25789 M 169.9 0 32 (steps accomplish the image data compression. But a) W 300 -26889 M 64.7 0 32 (good deal of the JPEG proposal is also concerned with) W 300 -27989 M 15.3 0 32 (the handling and control of color \(or other\) images with) W 300 -29089 M 460.0 0 32 (multiple components. JPEG's aim for a generic) W 300 -30189 M 871.8 0 32 (compression standard requires its proposal to) W 300 -31289 M (accommodate a variety of source image formats.) h 300 -32389 M 300 -33489 M /Times-Bold-ISOLatin1 F 1000 o f (6.1 Source Image Formats) h 300 -35189 M /Times-Roman-ISOLatin1 F 1000 o f 95.4 0 32 (The source image model used in the JPEG proposal is) W 300 -36289 M 388.9 0 32 (an abstraction from a variety of image types and) W 300 -37389 M 138.6 0 32 (applications and consists of only what is necessary to) W 300 -38489 M 365.0 0 32 (compress and reconstruct digital image data. The) W 300 -39589 M 35.9 0 32 (reader should recognize that the JPEG compressed data) W 300 -40689 M 55.5 0 32 (format does not encode enough information to serve as) W 300 -41789 M 130.9 0 32 (a complete image representation. For example, JPEG) W 300 -42889 M 201.3 0 32 (does not specify or encode any information on pixel) W 300 -43989 M 694.3 0 32 (aspect ratio, color space, or image acquisition) W 300 -45089 M (characteristics.) h -31919 25472 T S N S 32030 -42311 22818 15439 @ I N 32030 -26872 T N S 3275 -15063 M /Times-Roman-ISOLatin1 F 1000 o f (Table 1. Predictors for Lossless Coding) h R S 3737 -1354 M /Times-Roman-ISOLatin1 F 1000 o f (selection\255) h R S 3737 -2313 M /Times-Roman-ISOLatin1 F 1000 o f (value) h R S 12462 -2313 M /Times-Roman-ISOLatin1 F 1000 o f (prediction) h R S 5271 -4038 M /Times-Roman-ISOLatin1 F 1000 o f (0) h R S 12654 -4038 M /Times-Roman-ISOLatin1 F 1000 o f (no prediction) h R S 5271 -5284 M /Times-Roman-ISOLatin1 F 1000 o f (1) h R S 5271 -6530 M /Times-Roman-ISOLatin1 F 1000 o f (2) h R S 5271 -7776 M /Times-Roman-ISOLatin1 F 1000 o f (3) h R S 5271 -9022 M /Times-Roman-ISOLatin1 F 1000 o f (4) h R S 5271 -10268 M /Times-Roman-ISOLatin1 F 1000 o f (5) h R S 5271 -11514 M /Times-Roman-ISOLatin1 F 1000 o f (6) h R S 5271 -12760 M /Times-Roman-ISOLatin1 F 1000 o f (7) h R S 12941 -5284 M /Times-Roman-ISOLatin1 F 1000 o f (A) h R S 12941 -6530 M /Times-Roman-ISOLatin1 F 1000 o f (B) h R S 12941 -7776 M /Times-Roman-ISOLatin1 F 1000 o f (C) h R S 12941 -9022 M /Times-Roman-ISOLatin1 F 1000 o f (A+B\255C) h R S 12941 -10268 M /Times-Roman-ISOLatin1 F 1000 o f (A+\(\(B\255C\)/2\)) h R S 12941 -11514 M /Times-Roman-ISOLatin1 F 1000 o f (B+\(\(A\255C\)/2\)) h R S 12941 -12760 M /Times-Roman-ISOLatin1 F 1000 o f (\(A+B\)/2) h R S 2980 -13017 16683 12878 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S N 3059.00 -2678.00 M 19742.00 -2678.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R R R R S 5321 -7623 T N S 0 -18886 50333 18886 @ R 0 G 300 -1050 M 300 -18265 M S 0 -18886 50333 18886 @ R -5321 7623 T S N S 6040 -24842 48895 15819 @ I N 6040 -9023 T N S 14805 -7446 6419 3372 @ S 75 w 0 c 0 j 2 i 0.00 G k R R S 24485 -7365 6419 3371 @ S 75 w 0 c 0 j 2 i 0.00 G k R R S 6605 -7830 4592 4239 @ S 75 w 0 c 0 j 2 i 0.00 G k R R S N 21194.00 -5693.00 M 24379.00 -5693.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 23924.00 -5947.00 M 24468.00 -5693.00 L 23924.00 -5440.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 12919 -8253 19869 5301 @ S 400 w 0 c 0 j 0.875 G k R R S 16371 -6156 M /Times-Roman-ISOLatin1 F 1000 o f (Predictor) h R S 25955 -5348 M /Times-Roman-ISOLatin1 F 1000 o f (Entropy) h R S 25955 -6718 M /Times-Roman-ISOLatin1 F 1000 o f (Encoder) h R S 34036 -6700 9118 1720 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S 20155 -2341 M /Times-Roman-ISOLatin1 F 1000 o f (Lossless Encoder) h R S N 27860.00 -9526.00 M 27860.00 -7553.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 28113.00 -8038.00 M 27859.00 -7494.00 L 27606.00 -8038.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 11310.00 -5934.00 M 14736.00 -5934.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 14252.00 -6188.00 M 14795.00 -5934.00 L 14252.00 -5681.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 30770.00 -5853.00 M 34015.00 -5853.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 33531.00 -6107.00 M 34074.00 -5853.00 L 33531.00 -5600.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S 7346 -10432 M /Times-Roman-ISOLatin1 F 1000 o f ( Source ) h R S 6805 -11556 M /Times-Roman-ISOLatin1 F 1000 o f (Image Data) h R S 25926 -10814 M /Times-Roman-ISOLatin1 F 1000 o f ( Table) h R S 24948 -11967 M /Times-Roman-ISOLatin1 F 1000 o f ( Specifications) h R S 36573 -10348 M /Times-Roman-ISOLatin1 F 1000 o f (Compressed) h R S 36253 -11503 M /Times-Roman-ISOLatin1 F 1000 o f ( Image Data) h R S 15111 -15567 M /Times-Roman-ISOLatin1 F 1000 o f (Figure 4. Lossless Mode Encoder Processing Steps) h R S 24157 -12561 7441 2856 @ S 50 w 0 c 0 j 2 i 0.00 G k R R R R R S 30679 -76122 M /Times-Roman-ISOLatin1 F 1000 o f (7) h R showpage $P e %%Page: 8 8 /$P a D g N 0 79200 T S R S 6314 -26079 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 129.3 0 32 (Figure 6 illustrates the JPEG source image model. A) W 300 -2150 M 733.9 0 32 (source image contains from 1 to 255 image) W 300 -3250 M 143.3 0 32 (components, sometimes called color or spectral bands) W 300 -4350 M 59.1 0 32 (or channels. Each component consists of a rectangular) W 300 -5450 M 369.4 0 32 (array of samples. A sample is defined to be an) W 300 -6550 M 121.1 0 32 (unsigned integer with precision P bits, with any value) W 300 -7650 M 110.9 0 32 (in the range [0, 2) W n 0.800 o f 0.0 448.0 m 110.9 0 32 (P) W 0 -448.0 m n 1.250 o f 110.9 0 32 (\2551]. All samples of all components) W 300 -8750 M 305.4 0 32 (within the same source image must have the same) W 300 -9850 M 113.6 0 32 (precision P. P can be 8 or 12 for DCT\255based codecs,) W 300 -10950 M (and 2 to 16 for predictive codecs.) h 300 -12050 M 300 -13150 M 35.8 0 32 (The ith component has sample dimensions x) W n 0.800 o f 0.0 -358.0 m 35.8 0 32 (i) W 0 358.0 m n 1.250 o f 35.8 0 32 ( by y) W n 0.800 o f 0.0 -358.0 m 35.8 0 32 (i) W 0 358.0 m n 1.250 o f 35.8 0 32 (. To) W 300 -14250 M 960.8 0 32 (accommodate formats in which some image) W 300 -15350 M 119.1 0 32 (components are sampled at different rates than others,) W 300 -16450 M 504.5 0 32 (components can have different dimensions. The) W 300 -17550 M 258.7 0 32 (dimensions must have a mutual integral relationship) W 300 -18650 M 392.4 0 32 (defined by H) W n 0.800 o f 0.0 -358.0 m 392.4 0 32 (i) W 0 358.0 m n 1.250 o f 392.4 0 32 ( and V) W n 0.800 o f 0.0 -358.0 m 392.4 0 32 (i) W 0 358.0 m n 1.250 o f 392.4 0 32 (, the relative horizontal and) W 300 -19750 M 134.9 0 32 (vertical sampling factors, which must be specified for) W 300 -20850 M 128.4 0 32 (each component. Overall image dimensions X and Y) W 300 -21950 M 533.9 0 32 (are defined as the maximum x) W n 0.800 o f 0.0 -358.0 m 533.9 0 32 (i) W 0 358.0 m n 1.250 o f 533.9 0 32 ( and y) W n 0.800 o f 0.0 -358.0 m 533.9 0 32 (i) W 0 358.0 m n 1.250 o f 533.9 0 32 ( for all) W 300 -23050 M 36.0 0 32 (components in the image, and can be any number up to) W 300 -24150 M 184.8 0 32 (2) W n 0.800 o f 0.0 448.0 m 184.8 0 32 (16) W 0 -448.0 m n 1.250 o f 184.8 0 32 (. H and V are allowed only the integer values 1) W 300 -25250 M 86.3 0 32 (through 4. The encoded parameters are X, Y, and H) W n 0.800 o f 0.0 -358.0 m 86.3 0 32 (i) W 0 358.0 m n 1.250 o f 86.3 0 32 (s) W 300 -26350 M 3.8 0 32 (and V) W n 0.800 o f 0.0 -358.0 m 3.8 0 32 (i) W 0 358.0 m n 1.250 o f 3.8 0 32 (s for each components. The decoder reconstructs) W 300 -27450 M 17.4 0 32 (the dimensions x) W n 0.800 o f 0.0 -358.0 m 17.4 0 32 (i) W 0 358.0 m n 1.250 o f 17.4 0 32 ( and y) W n 0.800 o f 0.0 -358.0 m 17.4 0 32 (i) W 0 358.0 m n 1.250 o f 17.4 0 32 ( for each component, according) W 300 -28550 M (to the following relationship shown in Equation 5:) h 300 -35499 M 300 -36599 M /Times-Roman-ISOLatin1 F 1000 o f (where ) h /Symbol F 1000 o f (\351 \371) h /Times-Roman-ISOLatin1 F 1000 o f ( is the ceiling function.) h 300 -37699 M 300 -38799 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1000 o f (6.2 Encoding Order and Interleaving) h 300 -40499 M /Times-Roman-ISOLatin1 F 1000 o f 157.3 0 32 (A practical image compression standard must address) W 300 -41599 M 188.0 0 32 (how systems will need to handle the data during the) W 300 -42699 M 111.0 0 32 (process of decompression. Many applications need to) W 300 -43799 M 749.5 0 32 (pipeline the process of displaying or printing) W 300 -44899 M 36.7 0 32 (multiple\255component images in parallel with the process) W -6314 26079 T S N S 6616 -60828 22435 5849 @ I N 6616 -54979 T N S 3793 -2015 M /Dutch801-Italic-DECmath_Italic F 1000 o f (x) h R S 4326 -2266 M /Dutch801-Italic-DECmath_Italic F 1000 o f (i) h R S 5082 -1922 M /Times-Roman-ISOLatin1 F 1000 o f (=) h R S 6926 -1947 M /Dutch801-Roman-DECmath_Symbol F 1253 o f (d) h /Dutch801-Italic-DECmath_Italic F 1000 o f (X) h /Times-Roman-ISOLatin1 F 1200 o f ( ) h /Courier-ISOLatin1 $ /Courier & P /Courier-ISOLatin1 F 1200 o f ( ) h % /AvantGarde-Book-ISOLatin1 $ % /AvantGarde-Book & P % /AvantGarde-Book-ISOLatin1 F 1200 o f % ( ) h % /Courier-ISOLatin1 F 1200 o f ( ) h /Dutch801-Roman-DECmath_Symbol F 1200 o f (e) h R S 10345 -1067 M /Dutch801-Italic-DECmath_Italic F 1000 o f (H) h R S 11067 -1412 M /Dutch801-Italic-DECmath_Italic F 1000 o f (i) h R S 9790 -2540 M /Dutch801-Italic-DECmath_Italic F 1000 o f (H) h R S N 9502.00 -1510.00 M 11557.00 -1510.00 L S 49 w 0 c 0 j 2 i 0.00 G k R R S 12670 -2114 M /Times-Roman-ISOLatin1 F 1200 o f ( and) h n 0.833 o f ( ) h R S 3876 -4899 M /Dutch801-Italic-DECmath_Italic F 1000 o f (y) h R S 4409 -5150 M /Dutch801-Italic-DECmath_Italic F 1000 o f (i) h R S 5165 -4806 M /Times-Roman-ISOLatin1 F 1000 o f (=) h R S 7584 -4899 M /Dutch801-Italic-DECmath_Italic F 1000 o f (Y) h R S 10363 -4046 M /Dutch801-Italic-DECmath_Italic F 1000 o f (V) h R S 10974 -4296 M /Dutch801-Italic-DECmath_Italic F 1000 o f (i) h R S 9807 -5424 M /Dutch801-Italic-DECmath_Italic F 1000 o f (V) h R S 10418 -5466 M /Dutch801-Italic-DECmath_Italic F 800 o f (m) h R S 12135 -4719 M /Dutch801-Roman-DECmath_Symbol F 1200 o f (e) h R S 11057 -5498 M /Dutch801-Italic-DECmath_Italic F 800 o f (ax) h R S 10610 -2588 M /Dutch801-Italic-DECmath_Italic F 800 o f (m) h R S 11249 -2620 M /Dutch801-Italic-DECmath_Italic F 800 o f (ax) h R S N 9885.00 -4388.00 M 11940.00 -4388.00 L S 49 w 0 c 0 j 2 i 0.00 G k R R S 7009 -4707 M /Dutch801-Roman-DECmath_Symbol F 1200 o f (d) h R S 8505 -4699 M /Dutch801-Roman-DECmath_Symbol F 1084 o f (\242) h R S 8410 -1822 M /Dutch801-Roman-DECmath_Symbol F 1084 o f (\242) h R S 21132 -5513 M /Times-Roman-ISOLatin1 F 1000 o f (\(5\)) h R R R R S 31919 -26075 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 F 1000 o f 305.0 0 32 (of decompression. For many systems, this is only) W 300 -2150 M 370.5 0 32 (feasible if the components are interleaved together) W 300 -3250 M (within the compressed data stream.) h 300 -4350 M 300 -5450 M 35.7 0 32 (To make the same interleaving machinery applicable to) W 300 -6550 M 439.7 0 32 (both DCT\255based and predictive codecs, the JPEG) W 300 -7650 M 25.1 0 32 (proposal has defined the concept of ) W 25.1 0 32 (\026) W 25.1 0 32 (data unit.) W 25.1 0 32 (\027) W 25.1 0 32 ( A data) W 300 -8750 M 83.2 0 32 (unit is a sample in predictive codecs and an 8x8 block) W 300 -9850 M (of samples in DCT\255based codecs.) h 300 -10950 M 300 -12050 M 40.2 0 32 (The order in which compressed data units are placed in) W 300 -13150 M 400.9 0 32 (the compressed data stream is a generalization of) W 300 -14250 M 274.3 0 32 (raster\255scan order. Generally, data units are ordered) W 300 -15350 M 231.2 0 32 (from left\255to\255right and top\255to\255bottom according to the) W 300 -16450 M 92.1 0 32 (orientation shown in Figure 6. \(It is the responsibility) W 300 -17550 M 21.7 0 32 (of applications to define which edges of a source image) W 300 -18650 M 36.0 0 32 (are top, bottom, left and right.\) If an image component) W 300 -19750 M 555.2 0 32 (is noninterleaved \(i.e., compressed without being) W 300 -20850 M 222.2 0 32 (interleaved with other components\), compressed data) W 300 -21950 M 250.1 0 32 (units are ordered in a pure raster scan as shown in) W 300 -23050 M (Figure 7.) h 300 -35752 M 300 -36852 M /Times-Roman-ISOLatin1 F 1000 o f 190.7 0 32 (When two or more components are interleaved, each) W 300 -37952 M 75.1 0 32 (component C) W n 0.800 o f 0.0 -358.0 m 75.1 0 32 (i) W 0 358.0 m n 1.250 o f 75.1 0 32 ( is partitioned into rectangular regions of) W 300 -39052 M 376.4 0 32 (H) W n 0.800 o f 0.0 -358.0 m 376.4 0 32 (i) W 0 358.0 m n 1.250 o f 376.4 0 32 ( by V) W n 0.800 o f 0.0 -358.0 m 376.4 0 32 (i) W 0 358.0 m n 1.250 o f 376.4 0 32 ( data units, as shown in the generalized) W 300 -40152 M 228.3 0 32 (example of Figure 8. Regions are ordered within a) W 300 -41252 M 288.4 0 32 (component from left\255to\255right and top\255to\255bottom, and) W 300 -42352 M 17.4 0 32 (within a region, data units are ordered from left\255to\255right) W 300 -43452 M 293.3 0 32 (and top\255to\255bottom. The JPEG proposal defines the) W 300 -44552 M 131.4 0 32 (term Minimum Coded Unit \(MCU\) to be the smallest) W -31919 26075 T S N S 32126 -61077 22626 11602 @ I N 32126 -49475 T N S N 5326.00 -7291.00 M 5326.00 -1714.00 L 16831.00 -1714.00 L 16831.00 -7204.00 L S 100 w 0 c 0 j 2 i 0.00 G k R R S N 7068.00 -1801.00 M 7068.00 -7291.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 5413.00 -3369.00 M 16744.00 -3369.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 8725.00 -1801.00 M 8725.00 -7291.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 10294.00 -1801.00 M 10294.00 -7291.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 11950.00 -1801.00 M 11950.00 -7291.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 13606.00 -1801.00 M 13606.00 -7291.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 15262.00 -1801.00 M 15262.00 -7291.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 6023.00 -2761.00 M 15841.00 -2761.00 L S 0.00 G - + * E R S 50 w 0 c 0 j 2 i 0.00 G k R R S N 15357.00 -3015.00 M 15900.00 -2761.00 L 15357.00 -2508.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 6023.00 -4329.00 M 15841.00 -4329.00 L S 0.00 G - + * E R S 50 w 0 c 0 j 2 i 0.00 G k R R S N 15357.00 -4583.00 M 15900.00 -4329.00 L 15357.00 -4076.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 6023.00 -5897.00 M 15912.00 -5897.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 15392.00 -6151.00 M 15936.00 -5897.00 L 15392.00 -5644.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S 10885 -1242 M /Times-Roman-ISOLatin1 F 1000 o f (top) h R S 17405 -4502 M /Times-Roman-ISOLatin1 F 1000 o f (right) h R S 9927 -8623 M /Times-Roman-ISOLatin1 F 1000 o f (bottom) h R S 3407 -4598 M /Times-Roman-ISOLatin1 F 1000 o f (left) h R S 2930 -10983 M /Times-Roman-ISOLatin1 F 1000 o f (Figure 7. Noninterleaved Data Ordering) h R S N 5413.00 -5198.00 M 16744.00 -5198.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 5413.00 -6593.00 M 16744.00 -6593.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S 5962 -3048 M /Symbol F 1200 o f (\267) h R S 7792 -3048 M /Symbol F 1200 o f (\267) h R S 9449 -3048 M /Symbol F 1200 o f (\267) h R S 11017 -3048 M /Symbol F 1200 o f (\267) h R S 12499 -3048 M /Symbol F 1200 o f (\267) h R S 14329 -3048 M /Symbol F 1200 o f (\267) h R S 5962 -4617 M /Symbol F 1200 o f (\267) h R S 7792 -4617 M /Symbol F 1200 o f (\267) h R S 9449 -4617 M /Symbol F 1200 o f (\267) h R S 11017 -4617 M /Symbol F 1200 o f (\267) h R S 12499 -4617 M /Symbol F 1200 o f (\267) h R S 14329 -4617 M /Symbol F 1200 o f (\267) h R S 5962 -6185 M /Symbol F 1200 o f (\267) h R S 7792 -6185 M /Symbol F 1200 o f (\267) h R S 9449 -6185 M /Symbol F 1200 o f (\267) h R S 11017 -6185 M /Symbol F 1200 o f (\267) h R S 12499 -6185 M /Symbol F 1200 o f (\267) h R S 14329 -6185 M /Symbol F 1200 o f (\267) h R S 15724 -6185 M /Symbol F 1200 o f (\267) h R S 15637 -4617 M /Symbol F 1200 o f (\267) h R S 15810 -3048 M /Symbol F 1200 o f (\267) h R S N 15985.00 -2880.00 M 6358.00 -4181.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 6839.00 -3860.00 M 6334.00 -4184.00 L 6907.00 -4362.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 15985.00 -4361.00 M 6358.00 -5663.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 6839.00 -5342.00 M 6334.00 -5666.00 L 6907.00 -5844.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 15724.00 -6016.00 M 7839.00 -7057.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 8321.00 -6738.00 M 7815.00 -7060.00 L 8388.00 -7240.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R R R R S 6136 -6135 T N 0 G 300 -1050 M 300 -19032 M -6136 6135 T S N S 6375 -24121 48416 16586 @ I N 6375 -7535 T N S 9244 -9158 9699 8966 @ S 100 w 0 c 0 j 2 i 0.00 G k R R S 7415 -9798 9701 4928 @ S 0.00 G - + * E R S 100 w 0 c 0 j 2 i 0.00 G k R R S 27825 -11568 8505 8975 @ S 0.00 G - + * E R S 75 w 0 c 0 j 2 i 0.00 G k R R S 28301 -3210 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 29302 -3210 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 30374 -3210 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 31445 -3210 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 32517 -3210 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 33518 -3210 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 34591 -3210 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 35735 -3210 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 28301 -4190 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 29302 -4190 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 30374 -4190 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 31445 -4190 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 32517 -4190 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 33518 -4190 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 34591 -4190 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 35735 -4190 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 28230 -6603 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 29302 -6603 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 30374 -5473 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 31445 -5473 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 28230 -7584 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 29302 -5473 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 28230 -5473 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S N 33185.00 -2692.00 M 33185.00 -11468.00 L S 10 w 0 c 0 j 2 i 0.00 G k R R S N 32932.00 -10937.00 M 33185.00 -11481.00 L 33439.00 -10937.00 L S 10 w 0 c 0 j 2 i 0.00 G k R R S N 33439.00 -3224.00 M 33185.00 -2680.00 L 32932.00 -3224.00 L S 10 w 0 c 0 j 2 i 0.00 G k R R S N 27921.00 -9380.00 M 36378.00 -9380.00 L S 10 w 0 c 0 j 2 i 0.00 G k R R S N 35847.00 -9634.00 M 36391.00 -9380.00 L 35847.00 -9127.00 L S 10 w 0 c 0 j 2 i 0.00 G k R R S N 28453.00 -9127.00 M 27909.00 -9380.00 L 28453.00 -9634.00 L S 10 w 0 c 0 j 2 i 0.00 G k R R S 32614 -7043 1071 1132 @ S 0.00 G - + * E R R S 29397 -9833 929 981 @ S 0.00 G - + * E R R S 29540 -9442 M /Times-Roman-ISOLatin1 F 1000 o f (x) h 0.0 -448.0 m (i) h 0 448.0 m R S 32900 -6502 M /Times-Roman-ISOLatin1 F 1000 o f (y) h 0.0 -448.0 m (i) h 0 448.0 m R S 31685 -2094 M /Times-Roman-ISOLatin1 F 1000 o f (top) h R S 30970 -12654 M /Times-Roman-ISOLatin1 F 1000 o f (bottom) h R S 36830 -7675 M /Times-Roman-ISOLatin1 F 1000 o f (right) h R S 26252 -7752 M /Times-Roman-ISOLatin1 F 1000 o f (left) h R S 23751 -3752 M /Times-Roman-ISOLatin1 F 1000 o f (samples) h R S 37688 -3603 M /Times-Roman-ISOLatin1 F 1000 o f (line) h R S N 26793.00 -3738.00 M 28252.00 -4159.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 27716.00 -4268.00 M 28309.00 -4176.00 L 27857.00 -3782.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 26824.00 -3725.00 M 28176.00 -5295.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 27668.00 -5093.00 M 28215.00 -5340.00 L 28052.00 -4762.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 27538.00 -4289.00 M 27538.00 -3950.00 27538.00 -3950.00 32076.00 -3950.00 C 36615.00 -3950.00 36615.00 -3950.00 36615.00 -4289.00 C 36615.00 -4629.00 36615.00 -4629.00 32076.00 -4629.00 C 27538.00 -4629.00 27538.00 -4629.00 27538.00 -4289.00 C H S 50 w 0 c 0 j 2 i 0.00 G k R R S N 37402.00 -3725.00 M 36787.00 -4114.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 37061.00 -3641.00 M 36737.00 -4146.00 L 37332.00 -4070.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S 6863 -13926 M /Times-Roman-ISOLatin1 F 1000 o f (\(a\) Source image with multiple components ) h R S 6402 -11015 5472 4631 @ S 0.00 G - + * E R S 100 w 0 c 0 j 2 i 0.00 G k R R S 6248 -6138 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 7002 -5149 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 6658 -5639 M /Times-Roman-ISOLatin1 F 1000 o f (.) h R S 28040 -1901 M /Times-Roman-ISOLatin1 F 1000 o f (C) h 0.0 -448.0 m (i) h 0 448.0 m R S 17439 -16309 M /Times-Roman-ISOLatin1 F 1000 o f (Figure 6. JPEG Source Image Model) h R S 11849 -11761 M /Times-Roman-ISOLatin1 F 1000 o f (C) h 0.0 -448.0 m (1) h 0 448.0 m R S 12308 -10629 M /Times-Roman-ISOLatin1 F 1000 o f (C) h 0.0 -448.0 m (2) h 0 448.0 m R S 17920 -10345 M /Times-Roman-ISOLatin1 F 1000 o f (C) h 0.0 -448.0 m (Nf\2551) h 0 448.0 m R S 6022 -11388 5476 4632 @ S 0.00 G - + * E R S 100 w 0 c 0 j 2 i 0.00 G k R R S 25372 -13926 M /Times-Roman-ISOLatin1 F 1000 o f ( \(b\) Characteristics of an image component) h R S 14239 -10788 M /Times-Bold-ISOLatin1 F 1000 o f (.) h R S 15931 -10565 M /Times-Bold-ISOLatin1 F 1000 o f (.) h R S 17424 -10188 M /Times-Bold-ISOLatin1 F 1000 o f (.) h R S 20205 -9004 M /Times-Roman-ISOLatin1 F 1000 o f (C) h 0.0 -448.0 m (Nf) h 0 448.0 m R R R R S 30871 -76122 M /Times-Roman-ISOLatin1 F 1000 o f (8) h R showpage $P e %%Page: 9 9 /$P a D g N 0 79200 T S R S 6317 -38015 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 371.4 0 32 (group of interleaved data units. For the example) W 300 -2150 M 10.8 0 32 (shown, MCU) W n 0.800 o f 0.0 -358.0 m 10.8 0 32 (1) W 0 358.0 m n 1.250 o f 10.8 0 32 ( consists of data units taken first from the) W 300 -3250 M 50.4 0 32 (top\255left\255most region of C) W n 0.800 o f 0.0 -358.0 m 50.4 0 32 (1) W 0 358.0 m n 1.250 o f 50.4 0 32 (, followed by data units from) W 300 -4350 M 218.7 0 32 (the same region of C) W n 0.800 o f 0.0 -358.0 m 218.7 0 32 (2) W 0 358.0 m n 1.250 o f 218.7 0 32 (, and likewise for C) W n 0.800 o f 0.0 -358.0 m 218.7 0 32 (3) W 0 358.0 m n 1.250 o f 218.7 0 32 ( and C) W n 0.800 o f 0.0 -358.0 m 218.7 0 32 (4) W 0 358.0 m n 1.250 o f 218.7 0 32 (. ) W 300 -5450 M (MCU) h n 0.800 o f 0.0 -358.0 m (2) h 0 358.0 m n 1.250 o f ( continues the pattern as shown.) h 300 -6550 M 300 -7650 M 0.1 0 32 (Thus, interleaved data is an ordered sequence of MCUs,) W 300 -8750 M 122.0 0 32 (and the number of data units contained in an MCU is) W 300 -9850 M 175.8 0 32 (determined by the number of components interleaved) W 300 -10950 M 309.3 0 32 (and their relative sampling factors. The maximum) W 300 -12050 M 166.6 0 32 (number of components which can be interleaved is 4) W 300 -13150 M 105.2 0 32 (and the maximum number of data units in an MCU is) W 300 -14250 M 271.4 0 32 (10. The latter restriction is expressed as shown in) W 300 -15350 M 650.4 0 32 (Equation 6, where the summation is over the) W 300 -16450 M (interleaved components:) h 300 -21960 M /Times-Roman-ISOLatin1 F 1000 o f 86.6 0 32 (Because of this restriction, not every combination of 4) W 300 -23060 M 0.2 0 32 (components which can be represented in noninterleaved) W 300 -24160 M 170.4 0 32 (order within a JPEG\255compressed image is allowed to) W 300 -25260 M 312.3 0 32 (be interleaved. Also, note that the JPEG proposal) W 300 -26360 M 48.4 0 32 (allows some components to be interleaved and some to) W 300 -27460 M (be noninterleaved within the same compressed image.) h 300 -28560 M 300 -29660 M 300 -31360 M 300 -33060 M -6317 38015 T S N S 6715 -59225 22243 4410 @ I N 6715 -54815 T N S 6160 -1603 M /Symbol F 1200 o f (\345) h /Times-Roman-ISOLatin1 F 1000 o f ( H) h 0.0 -448.0 m (i) h 0 448.0 m ( \327 V) h 0.0 -448.0 m (i) h 0 448.0 m ( ) h /Symbol F 1000 o f (\243) h /Times-Roman-ISOLatin1 F 1000 o f ( 10) h R S 6063 -2753 M /Times-Italic-ISOLatin1 $ /Times-Italic & P /Times-Italic-ISOLatin1 F 800 o f (all ) h /Times-Roman-ISOLatin1 F 800 o f (i in) h R S 6063 -3520 M /Times-Roman-ISOLatin1 F 800 o f (interleave) h R S 21020 -3233 M /Times-Roman-ISOLatin1 F 1000 o f (\(6\)) h R R R R S 31919 -38038 T N 0 G 300 -1050 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1000 o f (6.3 Multiple Tables) h 300 -2750 M /Times-Roman-ISOLatin1 F 1000 o f 564.3 0 32 (In addition to the interleaving control discussed) W 300 -3850 M 235.7 0 32 (previously, JPEG codecs must control application of) W 300 -4950 M 166.7 0 32 (the proper table data to the proper components. The) W 300 -6050 M 178.4 0 32 (same quantization table and the same entropy coding) W 300 -7150 M 288.8 0 32 (table \(or set of tables\) must be used to encode all) W 300 -8250 M (samples within a component.) h 300 -9350 M 300 -10450 M 76.4 0 32 (JPEG decoders can store up to 4 different quantization) W 300 -11550 M 212.9 0 32 (tables and up to 4 different \(sets of\) entropy coding) W 300 -12650 M 632.8 0 32 (tables simultaneously. \(The Baseline sequential) W 300 -13750 M 93.3 0 32 (decoder is the exception; it can only store up to 2 sets) W 300 -14850 M 427.0 0 32 (of entropy coding tables.\) This is necessary for) W 300 -15950 M 1458.0 0 32 (switching between different tables during) W 300 -17050 M 916.2 0 32 (decompression of a scan containing multiple) W 300 -18150 M 111.1 0 32 (\(interleaved\) components, in order to apply the proper) W 300 -19250 M 322.9 0 32 (table to the proper component. \(Tables cannot be) W 300 -20350 M 302.0 0 32 (loaded during decompression of a scan.\) Figure 9) W 300 -21450 M 406.8 0 32 (illustrates the table\255switching control that must be) W 300 -22550 M 610.3 0 32 (managed in conjunction with multiple\255component) W 300 -23650 M 17.3 0 32 (interleaving for the encoder side. \(This simplified view) W 300 -24750 M 110.7 0 32 (does not distinguish between quantization and entropy) W 300 -25850 M (coding tables.\)) h -31919 38038 T R S 6136 -5992 T N 0 G 300 -1050 M 300 -31016 M -6136 5992 T S N S 6423 -35962 48128 28570 @ I N 6423 -7392 T N S N 3368.00 -10873.00 M 3368.00 -3107.00 L 14202.00 -3107.00 L 14202.00 -10873.00 L S 100 w 0 c 0 j 2 i 0.00 G k R R S N 3464.00 -6653.00 M 14297.00 -6653.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 7012.00 -3286.00 M 7012.00 -10693.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 10656.00 -3286.00 M 10656.00 -10693.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 14203.00 -3202.00 M 14203.00 -6750.00 L S 100 w 0 c 0 j 2 i 0.00 G k R R S N 3464.00 -10297.00 M 14297.00 -10297.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S 3848 -2854 M /Times-Roman-ISOLatin1 F 1000 o f ( 0 1 2 3 4 5) h R S 2410 -4196 M /Times-Roman-ISOLatin1 F 1000 o f (0) h R S 2410 -6112 M /Times-Roman-ISOLatin1 F 1000 o f (1) h R S 2410 -8028 M /Times-Roman-ISOLatin1 F 1000 o f (2) h R S 2410 -9944 M /Times-Roman-ISOLatin1 F 1000 o f (3) h R S N 16790.00 -7229.00 M 16790.00 -3106.00 L 27528.00 -3106.00 L 27528.00 -7133.00 L S 100 w 0 c 0 j 2 i 0.00 G k R R S 17460 -2758 M /Times-Roman-ISOLatin1 F 1000 o f (0 1 2 3 4 5) h R S 15927 -4196 M /Times-Roman-ISOLatin1 F 1000 o f (0) h R S 15927 -6112 M /Times-Roman-ISOLatin1 F 1000 o f (1) h R S N 20336.00 -3202.00 M 20336.00 -7133.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 23979.00 -3202.00 M 23979.00 -7133.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 16885.00 -6653.00 M 27527.00 -6653.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 30883.00 -10988.00 M 30883.00 -3202.00 L 36252.00 -3202.00 L 36252.00 -11064.00 L S 100 w 0 c 0 j 2 i 0.00 G k R R S N 30979.00 -6750.00 M 36348.00 -6750.00 L S 25 w 0 c 0 j 2 i 0.00 G k R R S N 32704.00 -3279.00 M 32704.00 -10910.00 L S 25 w 0 c 0 j 2 i 0.00 G k R R S N 30979.00 -10394.00 M 36348.00 -10394.00 L S 25 w 0 c 0 j 2 i 0.00 G k R R S N 34430.00 -3279.00 M 34430.00 -10910.00 L S 25 w 0 c 0 j 2 i 0.00 G k R R S 31458 -2854 M /Times-Roman-ISOLatin1 F 1000 o f ( 0 1 2) h R S 29924 -4196 M /Times-Roman-ISOLatin1 F 1000 o f (0) h R S 29924 -6113 M /Times-Roman-ISOLatin1 F 1000 o f (1) h R S 29924 -8028 M /Times-Roman-ISOLatin1 F 1000 o f (2) h R S 29924 -9944 M /Times-Roman-ISOLatin1 F 1000 o f (3) h R S N 40184.00 -7325.00 M 40184.00 -3202.00 L 45648.00 -3202.00 L 45648.00 -7325.00 L S 100 w 0 c 0 j 2 i 0.00 G k R R S N 40088.00 -4928.00 M 45552.00 -4928.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 42004.00 -3298.00 M 42004.00 -7133.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 43825.00 -3298.00 M 43825.00 -7133.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 40088.00 -6750.00 M 45552.00 -6750.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S 40854 -2854 M /Times-Roman-ISOLatin1 F 1000 o f (0 1 2) h R S 39320 -4484 M /Times-Roman-ISOLatin1 F 1000 o f (0) h R S 39320 -6400 M /Times-Roman-ISOLatin1 F 1000 o f (1) h R S 4482 -768 M /Times-Roman-ISOLatin1 F 1000 o f (Cs) h 0.0 -448.0 m (1) h 0 448.0 m (: H) h 0.0 -448.0 m (1) h 0 448.0 m (=2, V) h 0.0 -448.0 m (1) h 0 448.0 m (=2) h R S 17724 -863 M /Times-Roman-ISOLatin1 F 1000 o f (Cs) h 0.0 -448.0 m (2) h 0 448.0 m (: H) h 0.0 -448.0 m (2) h 0 448.0 m (=2, V) h 0.0 -448.0 m (2) h 0 448.0 m (=1) h R S 29128 -959 M /Times-Roman-ISOLatin1 F 1000 o f (Cs) h 0.0 -448.0 m (3) h 0 448.0 m (: H) h 0.0 -448.0 m (3) h 0 448.0 m (=1, V) h 0.0 -448.0 m (3) h 0 448.0 m (=2) h R S 38312 -864 M /Times-Roman-ISOLatin1 F 1000 o f (Cs) h 0.0 -448.0 m (4) h 0 448.0 m (: H) h 0.0 -448.0 m (4) h 0 448.0 m (=1, V) h 0.0 -448.0 m (4) h 0 448.0 m (=1) h R S 4235 -9678 M /Symbol F 1200 o f (\267) h R S 5961 -9678 M /Symbol F 1200 o f (\267) h R S 7591 -9678 M /Symbol F 1200 o f (\267) h R S 9604 -9678 M /Symbol F 1200 o f (\267) h R S 11522 -9678 M /Symbol F 1200 o f (\267) h R S 13439 -9678 M /Symbol F 1200 o f (\267) h R S 4235 -8048 M /Symbol F 1200 o f (\267) h R S 5961 -8048 M /Symbol F 1200 o f (\267) h R S 7591 -8048 M /Symbol F 1200 o f (\267) h R S 9604 -8048 M /Symbol F 1200 o f (\267) h R S 11426 -8048 M /Symbol F 1200 o f (\267) h R S 13439 -8048 M /Symbol F 1200 o f (\267) h R S 4235 -6131 M /Symbol F 1200 o f (\267) h R S 5961 -6131 M /Symbol F 1200 o f (\267) h R S 7591 -6131 M /Symbol F 1200 o f (\267) h R S 9604 -6131 M /Symbol F 1200 o f (\267) h R S 11522 -6131 M /Symbol F 1200 o f (\267) h R S 13439 -6131 M /Symbol F 1200 o f (\267) h R S 4235 -4501 M /Symbol F 1200 o f (\267) h R S 5961 -4501 M /Symbol F 1200 o f (\267) h R S 7591 -4501 M /Symbol F 1200 o f (\267) h R S 9604 -4501 M /Symbol F 1200 o f (\267) h R S 11618 -4597 M /Symbol F 1200 o f (\267) h R S 13439 -4501 M /Symbol F 1200 o f (\267) h R S N 4427.00 -4268.00 M 6153.00 -4268.00 L 4422.00 -5726.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 4629.00 -5220.00 M 4376.00 -5764.00 L 4956.00 -5608.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 4331.00 -5898.00 M 6057.00 -5898.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 6057.00 -5898.00 M 7654.00 -4302.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 7466.00 -4849.00 M 7671.00 -4285.00 L 7107.00 -4490.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 7975.00 -4268.00 M 9701.00 -4268.00 L 7970.00 -5726.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 8177.00 -5220.00 M 7924.00 -5764.00 L 8504.00 -5608.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 7879.00 -5898.00 M 9605.00 -5898.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 9605.00 -5898.00 M 11581.00 -4297.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 11337.00 -4821.00 M 11600.00 -4282.00 L 11018.00 -4427.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 11905.00 -4268.00 M 13631.00 -4268.00 L 11900.00 -5726.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 12107.00 -5220.00 M 11854.00 -5764.00 L 12434.00 -5608.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 11809.00 -5898.00 M 13535.00 -5898.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 4427.00 -7720.00 M 6153.00 -7720.00 L 4422.00 -9178.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 4629.00 -8672.00 M 4376.00 -9216.00 L 4956.00 -9060.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 4331.00 -9350.00 M 6057.00 -9350.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 6057.00 -9350.00 M 7654.00 -7754.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 7466.00 -8301.00 M 7671.00 -7737.00 L 7107.00 -7942.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S 40953 -4376 M /Symbol F 1200 o f (\267) h R S 17465 -6007 M /Symbol F 1200 o f (\267) h R S 19191 -6007 M /Symbol F 1200 o f (\267) h R S 21108 -6007 M /Symbol F 1200 o f (\267) h R S 22833 -6007 M /Symbol F 1200 o f (\267) h R S 24846 -6007 M /Symbol F 1200 o f (\267) h R S 26476 -6007 M /Symbol F 1200 o f (\267) h R S 17465 -4186 M /Symbol F 1200 o f (\267) h R S 19191 -4186 M /Symbol F 1200 o f (\267) h R S 21108 -4186 M /Symbol F 1200 o f (\267) h R S 22833 -4186 M /Symbol F 1200 o f (\267) h R S 24846 -4186 M /Symbol F 1200 o f (\267) h R S 26476 -4186 M /Symbol F 1200 o f (\267) h R S N 19287.00 -3884.00 M 21061.00 -3884.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 20541.00 -4138.00 M 21085.00 -3884.00 L 20541.00 -3631.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 23026.00 -3884.00 M 24800.00 -3884.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 24280.00 -4138.00 M 24824.00 -3884.00 L 24280.00 -3631.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 19383.00 -5706.00 M 21157.00 -5706.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 20637.00 -5960.00 M 21181.00 -5706.00 L 20637.00 -5453.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 26573.00 -3980.00 M 18182.00 -5409.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 18652.00 -5072.00 M 18158.00 -5414.00 L 18737.00 -5572.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S 31655 -4185 M /Symbol F 1200 o f (\267) h R S 33381 -4185 M /Symbol F 1200 o f (\267) h R S 35106 -4185 M /Symbol F 1200 o f (\267) h R S 31655 -6007 M /Symbol F 1200 o f (\267) h R S 33381 -6007 M /Symbol F 1200 o f (\267) h R S 35106 -6007 M /Symbol F 1200 o f (\267) h R S 31655 -8116 M /Symbol F 1200 o f (\267) h R S 33381 -8116 M /Symbol F 1200 o f (\267) h R S 35106 -8116 M /Symbol F 1200 o f (\267) h R S 31655 -9938 M /Symbol F 1200 o f (\267) h R S 33381 -9938 M /Symbol F 1200 o f (\267) h R S 35106 -9938 M /Symbol F 1200 o f (\267) h R S N 31847.00 -3980.00 M 31847.00 -5588.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 31594.00 -5104.00 M 31847.00 -5647.00 L 32101.00 -5104.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 33572.00 -3980.00 M 33572.00 -5588.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 33319.00 -5104.00 M 33572.00 -5647.00 L 33826.00 -5104.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 35298.00 -3980.00 M 35298.00 -5588.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 35045.00 -5104.00 M 35298.00 -5647.00 L 35552.00 -5104.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 31847.00 -7911.00 M 31847.00 -9519.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 31594.00 -9035.00 M 31847.00 -9578.00 L 32101.00 -9035.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 31846.00 -5802.00 M 33357.00 -4007.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 33213.00 -4573.00 M 33369.00 -3994.00 L 32825.00 -4246.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 33572.00 -5802.00 M 35083.00 -4007.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 34939.00 -4573.00 M 35095.00 -3994.00 L 34551.00 -4246.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 31942.00 -9637.00 M 33453.00 -7842.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 33309.00 -8408.00 M 33465.00 -7829.00 L 32921.00 -8081.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 35202.00 -5802.00 M 31685.00 -7798.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 32017.00 -7318.00 M 31669.00 -7807.00 L 32268.00 -7759.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 17561.00 -3884.00 M 19265.00 -3884.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 18781.00 -4138.00 M 19324.00 -3884.00 L 18781.00 -3631.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 17561.00 -5706.00 M 19265.00 -5706.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 18781.00 -5960.00 M 19324.00 -5706.00 L 18781.00 -5453.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 21108.00 -3884.00 M 22812.00 -3884.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 22328.00 -4138.00 M 22871.00 -3884.00 L 22328.00 -3631.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S 42679 -4376 M /Symbol F 1200 o f (\267) h R S 44500 -4376 M /Symbol F 1200 o f (\267) h R S 40953 -6293 M /Symbol F 1200 o f (\267) h R S 42679 -6293 M /Symbol F 1200 o f (\267) h R S 44500 -6293 M /Symbol F 1200 o f (\267) h R S N 42105.00 -4076.00 M 44850.00 -4076.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 44324.00 -4330.00 M 44868.00 -4076.00 L 44324.00 -3823.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 44789.00 -4172.00 M 41177.00 -5883.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 41544.00 -5429.00 M 41161.00 -5891.00 L 41761.00 -5887.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 41050.00 -6090.00 M 42549.00 -6090.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 42023.00 -6344.00 M 42567.00 -6090.00 L 42023.00 -5837.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 25039.00 -3884.00 M 26743.00 -3884.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 26259.00 -4138.00 M 26802.00 -3884.00 L 26259.00 -3631.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 16885.00 -5023.00 M 27527.00 -5023.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 13630.00 -6061.00 M 4855.00 -7491.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 5327.00 -7158.00 M 4831.00 -7496.00 L 5409.00 -7658.00 L S 20 w 0 c 0 j 2 i 0.00 G k R R S N 41183.00 -4034.00 M 42674.00 -4034.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S N 42148.00 -4288.00 M 42692.00 -4034.00 L 42148.00 -3781.00 L S 15 w 0 c 0 j 2 i 0.00 G k R R S /ctm_cached x y D N 20194.00 -8274.00 T 9817.00 15191.00 s 0 0 1 -68 -112 A ctm_cached t 0 c S 50 w 0 c 0 j 2 i 0.00 G k R R S 11023 -14203 M /Times-Roman-ISOLatin1 F 1000 o f (MCU) h 0.0 -448.0 m (1) h 0 448.0 m ( =) h R S 11023 -16599 M /Times-Roman-ISOLatin1 F 1000 o f (MCU) h 0.0 -448.0 m (2) h 0 448.0 m ( =) h R S 11023 -19090 M /Times-Roman-ISOLatin1 F 1000 o f (MCU) h 0.0 -448.0 m (3) h 0 448.0 m ( =) h R S 11023 -21294 M /Times-Roman-ISOLatin1 F 1000 o f (MCU) h 0.0 -448.0 m (4) h 0 448.0 m ( =) h R S 16717 -24638 M /Times-Roman-ISOLatin1 F 1000 o f (Cs) h 0.0 -448.0 m (1) h 0 448.0 m ( data units) h R S 25825 -24638 M /Times-Roman-ISOLatin1 F 1000 o f (Cs) h 0.0 -448.0 m (2) h 0 448.0 m ( ) h R S 29852 -24638 M /Times-Roman-ISOLatin1 F 1000 o f (Cs) h 0.0 -448.0 m (3) h 0 448.0 m ( ) h R S 33686 -24638 M /Times-Roman-ISOLatin1 F 1000 o f (Cs) h 0.0 -448.0 m (4) h 0 448.0 m R N S 16308 -15128 19255 2476 @ I N 16308 -12652 T N N S -574 -2646 20500 3339 @ I N -574 693 T N S 800 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 1400 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 1400 -2525 M /Times-Roman-ISOLatin1 F 800 o f (00) h R S 2400 -2083 M /Times-Roman-ISOLatin1 F 800 o f ( ) h R S 2700 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 3300 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 3300 -2525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 3800 -2534 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 4300 -2099 M /Times-Roman-ISOLatin1 F 1000 o f ( ) h R S 4600 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 5200 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 5200 -2534 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 5700 -2525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 6200 -2099 M /Times-Roman-ISOLatin1 F 1000 o f ( ) h R S 6500 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 7100 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 7100 -2534 M /Times-Roman-ISOLatin1 F 800 o f (11) h R S 8100 -2099 M /Times-Roman-ISOLatin1 F 1000 o f ( ) h R S 9000 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 9600 -1481 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 9600 -2525 M /Times-Roman-ISOLatin1 F 800 o f (00) h R S 10600 -2099 M /Times-Roman-ISOLatin1 F 1000 o f ( ) h R S 10900 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 11500 -1481 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 11500 -2525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 12000 -2534 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 12500 -2083 M /Times-Roman-ISOLatin1 F 800 o f ( ) h R S 13400 -2178 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 14000 -1476 M /Times-Roman-ISOLatin1 F 800 o f (3) h R S 14000 -2525 M /Times-Roman-ISOLatin1 F 800 o f (00) h R S 15000 -2099 M /Times-Roman-ISOLatin1 F 1000 o f ( ) h R S 15300 -2178 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 15900 -1476 M /Times-Roman-ISOLatin1 F 800 o f (3) h R S 15900 -2534 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 16400 -2525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 16900 -2099 M /Times-Roman-ISOLatin1 F 1000 o f ( ) h R S 17800 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 18400 -1481 M /Times-Roman-ISOLatin1 F 800 o f (4) h R S 18400 -2525 M /Times-Roman-ISOLatin1 F 800 o f (00) h R S 19400 -2099 M /Times-Roman-ISOLatin1 F 1000 o f (,) h R R R N S 16377 -17452 19254 2287 @ I N 16377 -15165 T N N S -575 -2476 20500 3339 @ I N -575 863 T N S 800 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 1400 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 1400 -2525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 1900 -2534 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 2400 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 2700 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 3300 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 3300 -2525 M /Times-Roman-ISOLatin1 F 800 o f (03) h R S 4300 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 4600 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 5200 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 5200 -2534 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 5700 -2525 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 6200 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 6500 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 7100 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 7100 -2534 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 7600 -2525 M /Times-Roman-ISOLatin1 F 800 o f (3) h R S 8100 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 9000 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 9600 -1481 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 9600 -2525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 10100 -2534 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 10600 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 10900 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 11500 -1481 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 11500 -2525 M /Times-Roman-ISOLatin1 F 800 o f (03) h R S 12500 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 13400 -2178 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 14000 -1476 M /Times-Roman-ISOLatin1 F 800 o f (3) h R S 14000 -2541 M /Times-Roman-ISOLatin1 F 1000 o f (0) h R S 14500 -2534 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 15000 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 15300 -2178 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 15900 -1476 M /Times-Roman-ISOLatin1 F 800 o f (3) h R S 15900 -2534 M /Times-Roman-ISOLatin1 F 800 o f (11) h R S 16900 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 17800 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 18400 -1481 M /Times-Roman-ISOLatin1 F 800 o f (4) h R S 18400 -2525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 18900 -2534 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 19400 -2099 M /Times-Roman-ISOLatin1 F 1200 o f (,) h R R R N S 16282 -19949 19447 2391 @ I N 16282 -17558 T N N S -478 -2511 20500 3347 @ I N -478 836 T N S 800 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 1400 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 1400 -2525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 1900 -2534 M /Times-Roman-ISOLatin1 F 800 o f (4) h R S 2400 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 2700 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 3300 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 3300 -2525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 3800 -2533 M /Times-Roman-ISOLatin1 F 800 o f (5) h R S 4300 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 4600 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 5200 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 5200 -2534 M /Times-Roman-ISOLatin1 F 800 o f (14) h R S 6200 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 6500 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 7100 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 7100 -2534 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 7600 -2533 M /Times-Roman-ISOLatin1 F 800 o f (5) h R S 8100 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 9000 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 9600 -1481 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 9600 -2525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 10100 -2534 M /Times-Roman-ISOLatin1 F 800 o f (4) h R S 10600 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 10900 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 11500 -1481 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 11500 -2525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 12000 -2533 M /Times-Roman-ISOLatin1 F 800 o f (5) h R S 12500 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 13400 -2178 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 14000 -1476 M /Times-Roman-ISOLatin1 F 800 o f (3) h R S 14000 -2525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 14500 -2534 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 15000 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 15300 -2178 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 15900 -1476 M /Times-Roman-ISOLatin1 F 800 o f (3) h R S 15900 -2534 M /Times-Roman-ISOLatin1 F 800 o f (12) h R S 16900 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 17800 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 18400 -1481 M /Times-Roman-ISOLatin1 F 800 o f (4) h R S 18400 -2525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 18900 -2534 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 19400 -2099 M /Times-Roman-ISOLatin1 F 1200 o f (,) h R R R N S 16282 -22537 19447 2391 @ I N 16282 -20146 T N N S -478 -2440 20500 3347 @ I N -478 907 T N S 800 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 1400 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 1400 -2525 M /Times-Roman-ISOLatin1 F 800 o f (20) h R S 2400 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 2700 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 3300 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 3300 -2541 M /Times-Roman-ISOLatin1 F 1000 o f (2) h R S 3800 -2533 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 4300 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 4600 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 5200 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 5200 -2534 M /Times-Roman-ISOLatin1 F 800 o f (30) h R S 6200 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 6500 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 7100 -1481 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 7100 -2534 M /Times-Roman-ISOLatin1 F 800 o f (3) h R S 7600 -2533 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 8100 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 9000 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 9600 -1481 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 9600 -2525 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 10100 -2534 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 10600 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 10900 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 11500 -1481 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 11500 -2525 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 12000 -2533 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 12500 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 13400 -2178 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 14000 -1476 M /Times-Roman-ISOLatin1 F 800 o f (3) h R S 14000 -2525 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 14500 -2534 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 15000 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 15300 -2178 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 15900 -1476 M /Times-Roman-ISOLatin1 F 800 o f (3) h R S 15900 -2534 M /Times-Roman-ISOLatin1 F 800 o f (30) h R S 16900 -2099 M /Times-Roman-ISOLatin1 F 1200 o f ( ) h R S 17800 -2179 M /Dutch801-Italic-DECmath_Italic F 1000 o f (d) h R S 18400 -1481 M /Times-Roman-ISOLatin1 F 800 o f (4) h R S 18400 -2525 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 18900 -2534 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 19400 -2099 M /Times-Roman-ISOLatin1 F 1200 o f (,) h R R R S /ctm_cached x y D N 26734.00 -20869.00 T 2089.00 2274.00 s 0 0 1 -41 -139 A ctm_cached t 0 c S 50 w 0 c 0 j 2 i 0.00 G k R R S /ctm_cached x y D N 30760.00 -20869.00 T 2089.00 2274.00 s 0 0 1 -41 -139 A ctm_cached t 0 c S 50 w 0 c 0 j 2 i 0.00 G k R R S /ctm_cached x y D N 34402.00 -20868.00 T 1454.00 1988.00 s 0 0 1 -41 -139 A ctm_cached t 0 c S 50 w 0 c 0 j 2 i 0.00 G k R R S 12817 -27196 M /Times-Roman-ISOLatin1 F 1000 o f (Figure 8. Generalized Interleaved Data Ordering Example) h R R R R S 30679 -75738 M /Times-Roman-ISOLatin1 F 1000 o f (9) h R showpage $P e %%Page: 10 10 /$P a D g N 0 79200 T S R S 6324 -5315 T N 0 G 300 -1050 M 300 -18735 M 300 -19835 M 300 -21085 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1200 o f 473.0 0 32 (7 Baseline and Other DCT Sequential) W 300 -22385 M (Codecs) h 300 -24135 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 97.0 0 32 (The DCT sequential mode of operation consists of the) W 300 -25235 M 135.1 0 32 (FDCT and Quantization steps from section 4, and the) W 300 -26335 M 481.0 0 32 (multiple\255component control from section 6.3. In) W 300 -27435 M 182.3 0 32 (addition to the Baseline sequential codec, other DCT) W 300 -28535 M 91.4 0 32 (sequential codecs are defined to accommodate the two) W 300 -29635 M 70.9 0 32 (different sample precisions \(8 and 12 bits\) and the two) W 300 -30735 M 240.7 0 32 (different types of entropy coding methods \(Huffman) W 300 -31835 M (and arithmetic\).) h 300 -32935 M 300 -34035 M 305.1 0 32 (Baseline sequential coding is for images with 8\255bit) W 300 -35135 M 67.8 0 32 (samples and uses Huffman coding only. It also differs) W 300 -36235 M 402.5 0 32 (from the other sequential DCT codecs in that its) W 300 -37335 M 40.2 0 32 (decoder can store only two sets of Huffman tables \(one) W 300 -38435 M 47.1 0 32 (AC table and DC table per set\). This restriction means) W 300 -39535 M 603.1 0 32 (that, for images with three or four interleaved) W 300 -40635 M 36.9 0 32 (components, at least one set of Huffman tables must be) W 300 -41735 M 149.0 0 32 (shared by two components. This restriction poses no) W 300 -42835 M 106.9 0 32 (limitation at all for noninterleaved components; a new) W 300 -43935 M 268.7 0 32 (set of tables can be loaded into the decoder before) W 300 -45035 M (decompression of a noninterleaved component begins.) h 300 -46135 M 300 -47235 M 313.3 0 32 (For many applications which do need to interleave) W 300 -48335 M 341.0 0 32 (three color components, this restriction is hardly a) W 300 -49435 M 467.9 0 32 (limitation at all. Color spaces \(YUV, CIELUV,) W 300 -50535 M 254.7 0 32 (CIELAB, and others\) which represent the chromatic) W 300 -51635 M 398.0 0 32 (\(``color''\) information in two components and the) W 300 -52735 M 278.2 0 32 (achromatic \(``grayscale''\) information in a third are) W 300 -53835 M 134.9 0 32 (more efficient for compression than spaces like RGB. ) W 300 -54935 M 95.9 0 32 (One Huffman table set can be used for the achromatic) W 300 -56035 M 162.0 0 32 (component and one for the chrominance components. ) W 300 -57135 M 805.3 0 32 (DCT coefficient statistics are similar for the) W 300 -58235 M 118.9 0 32 (chrominance components of most images, and one set) W 300 -59335 M 41.5 0 32 (of Huffman tables can encode both almost as optimally) W 300 -60435 M (as two.) h 300 -61535 M 300 -62635 M 448.1 0 32 (The committee also felt that early availability of) W 300 -63735 M 665.8 0 32 (single\255chip implementations at commodity prices) W 300 -64835 M 602.2 0 32 (would encourage early acceptance of the JPEG) W 300 -65935 M 203.6 0 32 (proposal in a variety of applications. In 1988 when) W -6324 5315 T S N S 4614 -23300 26461 16585 @ I N 4614 -6715 T N S 10111 -3956 M /Times-Roman-ISOLatin1 F 1000 o f (Encoding ) h R S 10191 -4798 M /Times-Roman-ISOLatin1 F 900 o f ( ) h n 1.111 o f (Process) h R S 3508 -2047 M /Times-Roman-ISOLatin1 F 900 o f ( ) h n 1.111 o f (A) h R S 3573 -4517 M /Times-Roman-ISOLatin1 F 900 o f ( ) h n 1.111 o f (B) h R S 3709 -6861 M /Times-Roman-ISOLatin1 F 900 o f ( ) h n 1.111 o f (C) h R S 3690 -2541 1239 1570 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S 3690 -4936 1239 1569 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S 3690 -7168 1239 1569 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S 9629 -5104 4697 2315 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S N 4995.00 -1881.00 M 6300.00 -1881.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 4995.00 -4111.00 M 6300.00 -4111.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 4995.00 -6423.00 M 6300.00 -6423.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S 8970 -10675 M /Times-Roman-ISOLatin1 F 1000 o f (Table) h n 0.900 o f ( ) h n 1.111 o f (Table ) h R S 12189 -12096 3325 2419 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S N 10543.00 -9759.00 M 10543.00 -8272.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 13458.00 -9484.00 M 13458.00 -8269.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 14262.00 -3945.00 M 17538.00 -3945.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 17054.00 -4199.00 M 17597.00 -3945.00 L 17054.00 -3692.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S /ctm_cached x y D N 8425.00 -4192.00 T 1276.00 1616.00 s 0 0 1 -133 -227 A ctm_cached t 0 c S 50 w 0 c 0 j 2 i 0.00 G k R R S N 7064.00 -5064.00 M 7573.00 -5381.00 L 7489.00 -4787.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 7469.00 -3594.00 M 7572.00 -3003.00 L 7053.00 -3304.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S /ctm_cached x y D N 12140.00 -4725.00 T 2711.00 3432.00 s 0 0 1 -61 -119 A ctm_cached t 0 c S 50 w 0 c 0 j 2 i 0.00 G k R R S N 13156.00 -8199.00 M 13486.00 -7698.00 L 12890.00 -7767.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 11389.00 -7778.00 M 10794.00 -7699.00 L 11115.00 -8205.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S 17720 -4729 5866 1568 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S 6168 -2114 M /Symbol F 900 o f (\267) h R S 6428 -3104 M /Symbol F 900 o f (\267) h R S 10348 -8419 M /Symbol F 900 o f (\267) h R S 13282 -8419 M /Symbol F 900 o f (\267) h R S N 11132.00 -8532.00 M 12239.00 -6798.00 L 12239.00 -5180.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 12493.00 -5665.00 M 12239.00 -5121.00 L 11986.00 -5665.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 6561.00 -2831.00 M 8194.00 -4069.00 L 9512.00 -4069.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S N 9028.00 -4323.00 M 9571.00 -4069.00 L 9028.00 -3816.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S 10998 -8638 M /Symbol F 900 o f (\267) h R S 18883 -10330 M /Times-Roman-ISOLatin1 F 1000 o f (Compressed ) h R S 18733 -11395 M /Times-Roman-ISOLatin1 F 900 o f ( ) h n 1.111 o f (Image Data) h R S 5462 -14680 M /Times-Roman-ISOLatin1 F 1000 o f (Figure 9. Component\255Interleave and ) h R S 3777 -10330 M /Times-Roman-ISOLatin1 F 1000 o f (Source ) h R S 2549 -11395 M /Times-Roman-ISOLatin1 F 900 o f ( ) h n 1.111 o f (Image Data) h R S 8745 -11663 M /Times-Roman-ISOLatin1 F 1000 o f (Spec. 1 ) h R S 12506 -11661 M /Times-Roman-ISOLatin1 F 1000 o f (Spec. 2) h R S 6168 -4371 M /Symbol F 900 o f (\267) h R S 6102 -6632 M /Symbol F 900 o f (\267) h R S 8427 -12096 3233 2419 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S 9584 -15926 M /Times-Roman-ISOLatin1 F 1000 o f (Table\255Switching Control) h R R R R S 31919 -7157 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 F 1000 o f 41.5 0 32 (Baseline sequential was defined, the committee's VLSI) W 300 -2150 M 43.6 0 32 (experts felt that current technology made the feasibility) W 300 -3250 M 126.6 0 32 (of crowding four sets of loadable Huffman tables \255 in) W 300 -4350 M 231.2 0 32 (addition to four sets of Quantization tables \255 onto a) W 300 -5450 M 983.0 0 32 (single commodity\255priced codec chip a risky) W 300 -6550 M (proposition.) h 300 -7650 M 300 -8750 M 41.7 0 32 (The FDCT, Quantization, DC differencing, and zig\255zag) W 300 -9850 M 231.3 0 32 (ordering processing steps for the Baseline sequential) W 300 -10950 M 119.4 0 32 (codec proceed just as described in section 4. Prior to) W 300 -12050 M 341.4 0 32 (entropy coding, there usually are few nonzero and) W 300 -13150 M 254.1 0 32 (many zero\255valued coefficients. The task of entropy) W 300 -14250 M 158.9 0 32 (coding is to encode these few coefficients efficiently. ) W 300 -15350 M 138.7 0 32 (The description of Baseline sequential entropy coding) W 300 -16450 M 46.0 0 32 (is given in two steps: conversion of the quantized DCT) W 300 -17550 M 157.3 0 32 (coefficients into an intermediate sequence of symbols) W 300 -18650 M 638.7 0 32 (and assignment of variable\255length codes to the) W 300 -19750 M (symbols.) h 300 -20850 M 300 -21950 M /Times-Bold-ISOLatin1 F 1000 o f (7.1 Intermediate Entropy Coding Representations) h 300 -23650 M /Times-Roman-ISOLatin1 F 1000 o f 47.7 0 32 (In the intermediate symbol sequence, each nonzero AC) W 300 -24750 M 435.0 0 32 (coefficient is represented in combination with the) W 300 -25850 M 128.2 0 32 (``runlength'' \(consecutive number\) of zero\255valued AC) W 300 -26950 M 151.1 0 32 (coefficients which precede it in the zig\255zag sequence. ) W 300 -28050 M (Each such runlength/nonzero\255coefficient combination is) h 300 -29150 M (\(usually\) represented by a pair of symbols:) h 300 -30250 M 300 -31350 M 5120 -31350 M (symbol\2551) h 15387 -31350 M (symbol\2552) h 300 -32450 M 2316 -32450 M (\(RUNLENGTH, SIZE\)) h 14055 -32450 M (\(AMPLITUDE\)) h 300 -33550 M 300 -34650 M 677.4 0 32 (Symbol\2551 represents two pieces of information, ) W 300 -35750 M 410.8 0 32 (RUNLENGTH and SIZE. Symbol\2552 represents the) W 300 -36850 M 166.4 0 32 (single piece of information designated AMPLITUDE,) W 300 -37950 M 339.9 0 32 (which is simply the amplitude of the nonzero AC) W 300 -39050 M 955.4 0 32 (coefficient. RUNLENGTH is the number of) W 300 -40150 M 83.7 0 32 (consecutive zero\255valued AC coefficients in the zig\255zag) W 300 -41250 M 167.0 0 32 (sequence preceding the nonzero AC coefficient being) W 300 -42350 M 61.7 0 32 (represented. SIZE is the number of bits used to encode) W 300 -43450 M 194.1 0 32 (AMPLITUDE \255 that is, to encoded symbol\2552, by the) W 300 -44550 M 272.0 0 32 (signed\255integer encoding used with JPEG's particular) W 300 -45650 M (method of Huffman coding. ) h 300 -46750 M 300 -47850 M 127.0 0 32 (RUNLENGTH represents zero\255runs of length 0 to 15.) W 300 -48950 M 35.3 0 32 (Actual zero\255runs in the zig\255zag sequence can be greater) W 300 -50050 M 66.5 0 32 (than 15, so the symbol\2551 value \(15, 0\) is interpreted as) W 300 -51150 M 85.9 0 32 (the extension symbol with runlength=16. There can be) W 300 -52250 M 191.0 0 32 (up to three consecutive \(15, 0\) extensions before the) W 300 -53350 M 555.0 0 32 (terminating symbol\2551 whose RUNLENGTH value) W 300 -54450 M 655.2 0 32 (completes the actual runlength. The terminating) W 300 -55550 M 293.1 0 32 (symbol\2551 is always followed by a single symbol\2552,) W 300 -56650 M 311.2 0 32 (except for the case in which the last run of zeros) W 300 -57750 M 100.6 0 32 (includes the last \(63d\) AC coefficient. In this frequent) W 300 -58850 M 34.8 0 32 (case, the special symbol\2551 value \(0,0\) means EOB \(end) W 300 -59950 M 129.9 0 32 (of block\), and can be viewed as an ``escape'' symbol) W 300 -61050 M (which terminates the 8x8 sample block.) h 300 -62150 M -31919 7157 T R S 30392 -75162 M /Times-Roman-ISOLatin1 F 1000 o f (10) h R showpage $P e %%Page: 11 11 /$P a D g N 0 79200 T S R S 6328 -7185 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 375.0 0 32 (Thus, for each 8x8 block of samples, the zig\255zag) W 300 -2150 M 805.5 0 32 (sequence of 63 quantized AC coefficients is) W 300 -3250 M 458.3 0 32 (represented as a sequence of symbol\2551, symbol\2552) W 300 -4350 M 79.4 0 32 (symbol pairs, though each ``pair'' can have repetitions) W 300 -5450 M 7.5 0 32 (of symbol\2551 in the case of a long run\255length or only one) W 300 -6550 M (symbol\2551 in the case of an EOB.) h 300 -7650 M 300 -8750 M 518.5 0 32 (The possible range of quantized AC coefficients) W 300 -9850 M 575.3 0 32 (determines the range of values which both the) W 300 -10950 M 793.8 0 32 (AMPLITUDE and the SIZE information must) W 300 -12050 M 388.7 0 32 (represent. A numerical analysis of the 8x8 FDCT) W 300 -13150 M 135.0 0 32 (equation shows that, if the 64\255point \(8x8 block\) input) W 300 -14250 M 235.8 0 32 (signal contains N\255bit integers, then the nonfractional) W 300 -15350 M 7.0 0 32 (part of the output numbers \(DCT coefficients\) can grow) W 300 -16450 M 95.5 0 32 (by at most 3 bits. This is also the largest possible size) W 300 -17550 M 69.5 0 32 (of a quantized DCT coefficient when its quantizer step) W 300 -18650 M (size has integer value 1.) h 300 -19750 M 300 -20850 M 83.1 0 32 (Baseline sequential has 8\255bit integer source samples in) W 300 -21950 M 381.9 0 32 (the range [\2552) W n 0.800 o f 0.0 448.0 m 381.9 0 32 (7) W 0 -448.0 m n 1.250 o f 381.9 0 32 (, 2) W n 0.800 o f 0.0 448.0 m 381.9 0 32 (7) W 0 -448.0 m n 1.250 o f 381.9 0 32 (\2551], so quantized AC coefficient) W 300 -23050 M 132.8 0 32 (amplitudes are covered by integers in the range [\2552) W n 0.800 o f 0.0 448.0 m 132.8 0 32 (10) W 0 -448.0 m n 1.250 o f 132.8 0 32 (,) W 300 -24150 M 406.4 0 32 (2) W n 0.800 o f 0.0 448.0 m 406.4 0 32 (10) W 0 -448.0 m n 1.250 o f 406.4 0 32 (\2551]. The signed\255integer encoding uses symbol\2552) W 300 -25250 M 71.9 0 32 (AMPLITUDE codes of 1 to 10 bits in length \(so SIZE) W 300 -26350 M 888.7 0 32 (also represents values from 1 to 10\), and) W 300 -27450 M 416.6 0 32 (RUNLENGTH represents values from 0 to 15 as) W 300 -28550 M 36.8 0 32 (discussed previously. For AC coefficients, the structure) W 300 -29650 M 1027.2 0 32 (of the symbol\2551 and symbol\2552 intermediate) W 300 -30750 M 547.3 0 32 (representations is illustrated in Tables 2 and 3,) W 300 -31850 M (respectively.) h 300 -32950 M 300 -34050 M 379.7 0 32 (The intermediate representation for an 8x8 sample) W 300 -35150 M 694.4 0 32 (block's differential DC coefficient is structured) W 300 -36250 M 310.6 0 32 (similarly. Symbol\2551, however, represents only SIZE) W 300 -37350 M 1027.0 0 32 (information; symbol\2552 represents AMPLITUDE) W 300 -38450 M (information as before:) h 300 -39550 M 300 -40650 M 3437 -40650 M (symbol\2551) h 13467 -40650 M (symbol\2552) h 300 -41750 M 3938 -41750 M (\(SIZE\)) h 12135 -41750 M (\(AMPLITUDE\)) h 300 -42850 M 300 -43950 M 63.6 0 32 (Because the DC coefficient is differentially encoded, it) W 300 -45050 M 323.6 0 32 (is covered by twice as many integer values, [\2552) W n 0.800 o f 0.0 448.0 m 323.6 0 32 (11) W 0 -448.0 m n 1.250 o f 323.6 0 32 (,) W 300 -46150 M 167.3 0 32 (2) W n 0.800 o f 0.0 448.0 m 167.3 0 32 (11) W 0 -448.0 m n 1.250 o f 167.3 0 32 (\2551] as the AC coefficients, so one additional level) W 300 -47250 M 366.4 0 32 (must be added to the bottom of Table 3 for DC) W 300 -48350 M 688.6 0 32 (coefficients. Symbol\2551 for DC coefficients thus) W 300 -49450 M (represents a value from 1 to 11.) h -6328 7185 T S N S 6152 -71270 23393 14285 @ I N 6152 -56985 T N S 9077 -3333 M /Times-Roman-ISOLatin1 F 1100 o f (0 1 2 . . . 9 10) h R S 1502 -7064 M /Times-Roman-ISOLatin1 F 1100 o f (RUN) h R S 6918 -4947 M /Times-Roman-ISOLatin1 F 1100 o f (0) h R S 6918 -6258 M /Times-Roman-ISOLatin1 F 1100 o f (.) h R S 6918 -7568 M /Times-Roman-ISOLatin1 F 1100 o f (.) h R S 6918 -8879 M /Times-Roman-ISOLatin1 F 1100 o f (.) h R S 6918 -10191 M /Times-Roman-ISOLatin1 F 1100 o f (15) h R S 9122 -6258 M /Times-Roman-ISOLatin1 F 1100 o f (X) h R S 9122 -7568 M /Times-Roman-ISOLatin1 F 1100 o f (X) h R S 9122 -8879 M /Times-Roman-ISOLatin1 F 1100 o f (X) h R S 8548 -4947 M /Times-Roman-ISOLatin1 F 1100 o f (EOB) h R S 8548 -10191 M /Times-Roman-ISOLatin1 F 1100 o f (ZRL) h R S 13199 -7064 M /Times-Roman-ISOLatin1 F 1100 o f (RUN\255SIZE) h R S 14061 -8071 M /Times-Roman-ISOLatin1 F 1100 o f (values) h R S 1502 -8071 M /Times-Roman-ISOLatin1 F 1100 o f (LENGTH) h R S 1166 -10594 20612 9500 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S N 1213.00 -3787.00 M 21826.00 -3787.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S 4762 -12349 M /Times-Roman-ISOLatin1 F 1000 o f (Table 2. Baseline Huffman Coding) h R S 8693 -13669 M /Times-Roman-ISOLatin1 F 1000 o f (Symbol\2551 Structure ) h R S 15084 -2303 M /Times-Roman-ISOLatin1 F 1100 o f (SIZE) h R S N 6215.00 -1174.00 M 6215.00 -10570.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R R R R S 31919 -7195 T N 0 G 300 -1050 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1000 o f (7.2 Variable\255Length Entropy Coding) h 300 -2750 M /Times-Roman-ISOLatin1 F 1000 o f 58.8 0 32 (Once the quantized coefficient data for an 8x8 block is) W 300 -3850 M 594.4 0 32 (represented in the intermediate symbol sequence) W 300 -4950 M 294.8 0 32 (described above, variable\255length codes are assigned. ) W 300 -6050 M 52.0 0 32 (For each 8x8 block, the DC coefficient's symbol\2551 and) W 300 -7150 M (symbol\2552 representation is coded and output first.) h 300 -8250 M 300 -9350 M 232.4 0 32 (For both DC and AC coefficients, each symbol\2551 is) W 300 -10450 M 194.6 0 32 (encoded with a variable\255length code \(VLC\) from the) W 300 -11550 M 180.4 0 32 (Huffman table set assigned to the 8x8 block's image) W 300 -12650 M 571.1 0 32 (component. Each symbol\2552 is encoded with a) W 300 -13750 M 194.7 0 32 (\026) W 194.7 0 32 (variable\255length integer) W 194.7 0 32 (\027) W 194.7 0 32 ( \(VLI\) code whose length in) W 300 -14850 M 11.4 0 32 (bits is given in Table 3. VLCs and VLIs both are codes) W 300 -15950 M 41.6 0 32 (with variable lengths, but VLIs are not Huffman codes. ) W 300 -17050 M 187.8 0 32 (An important distinction is that the length of a VLC) W 300 -18150 M 160.2 0 32 (\(Huffman code\) is not known until it is decoded, but) W 300 -19250 M (the length of a VLI is stored in its preceding VLC.) h 300 -20350 M 300 -21450 M 59.6 0 32 (Huffman codes \(VLCs\) must be specified externally as) W 300 -22550 M 235.9 0 32 (an input to JPEG encoders. \(Note that the form in) W 300 -23650 M 401.0 0 32 (which Huffman tables are represented in the data) W 300 -24750 M 400.6 0 32 (stream is an indirect specification with which the) W 300 -25850 M 170.4 0 32 (decoder must construct the tables themselves prior to) W 300 -26950 M 467.3 0 32 (decompression.\) The JPEG proposal includes an) W 300 -28050 M 10.3 0 32 (example set of Huffman tables in its information annex,) W 300 -29150 M 227.0 0 32 (but because they are application\255specific, it specifies) W 300 -30250 M 100.2 0 32 (none for required use. The VLI codes in contrast, are) W 300 -31350 M 289.6 0 32 (\026) W 289.6 0 32 (hardwired) W 289.6 0 32 (\027) W 289.6 0 32 ( into the proposal. This is appropriate,) W 300 -32450 M 105.3 0 32 (because the VLI codes are far more numerous, can be) W 300 -33550 M 79.9 0 32 (computed rather than stored, and have not been shown) W 300 -34650 M 99.3 0 32 (to be appreciably more efficient when implemented as) W 300 -35750 M (Huffman codes.) h 300 -36850 M 300 -37950 M /Times-Bold-ISOLatin1 F 1000 o f (7.3 Baseline Encoding Example) h 300 -39650 M /Times-Roman-ISOLatin1 F 1000 o f 43.4 0 32 (This section gives an example of Baseline compression) W 300 -40750 M 47.1 0 32 (and encoding of a single 8x8 sample block. Note that a) W 300 -41850 M 3.0 0 32 (good deal of the operation of a complete JPEG Baseline) W 300 -42950 M 708.2 0 32 (encoder is omitted here, including creation of) W 300 -44050 M 208.8 0 32 (Interchange Format information \(parameters, headers,) W 300 -45150 M 777.5 0 32 (quantization and Huffman tables\), byte\255stuffing,) W 300 -46250 M 52.1 0 32 (padding to byte\255boundaries prior to a marker code, and) W 300 -47350 M 64.5 0 32 (other key operations. Nonetheless, this example should) W 300 -48450 M 638.9 0 32 (help to make concrete much of the foregoing) W 300 -49550 M (explanation.) h 300 -50650 M 300 -51750 M 524.0 0 32 (Figure 10\(a\) is an 8x8 block of 8\255bit samples,) W 300 -52850 M 389.0 0 32 (aribtrarily extracted from a real image. The small) W 300 -53950 M 703.3 0 32 (variations from sample to sample indicate the) W 300 -55050 M 722.4 0 32 (predominance of low spatial frequencies. After) W 300 -56150 M 345.3 0 32 (subtracting 128 from each sample for the required) W 300 -57250 M 457.8 0 32 (level\255shift, the 8x8 block is input to the FDCT,) W 300 -58350 M 17.4 0 32 (equation \(1\). Figure 10\(b\) shows \(to one decimal place\)) W 300 -59450 M 68.0 0 32 (the resulting DCT coefficients. Except for a few of the) W 300 -60550 M 97.3 0 32 (lowest frequency coefficients, the amplitudes are quite) W 300 -61650 M (small.) h 300 -62750 M -31919 7195 T R S 30392 -75642 M /Times-Roman-ISOLatin1 F 1000 o f (11) h R showpage $P e %%Page: 12 12 /$P a D g N 0 79200 T S S 7200 -2700 T N 0 G 300 -1200 M -7200 2700 T R S 7200 -74700 T N 0 G 300 -1200 M -7200 74700 T R R S 7070 -42751 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 236.4 0 32 (Figure 10\(c\) is the example quantization table for) W 300 -2150 M 264.4 0 32 (luminance \(grayscale\) components included in the) W 300 -3250 M 101.6 0 32 (informational annex of the draft JPEG standard part) W 300 -4350 M 486.3 0 32 (1 [2]. Figure 10\(d\) shows the quantized DCT) W 300 -5450 M 214.4 0 32 (coefficients, normalized by their quantization table) W 300 -6550 M 106.4 0 32 (entries, as specified by equation \(3\). At the decoder) W 300 -7650 M 487.0 0 32 (these numbers are ) W 487.0 0 32 (\026) W 487.0 0 32 (denormalized) W 487.0 0 32 (\027) W 487.0 0 32 ( according to) W 300 -8750 M 206.8 0 32 (equation \(4\), and input to the IDCT, equation \(2\).) W 300 -9850 M 90.7 0 32 (Finally, figure 10\(f\) shows the reconstructed sample) W 300 -10950 M (values, remarkably similar to the originals in 10\(a\). ) h 300 -12050 M 300 -13150 M 331.9 0 32 (Of course, the numbers in figure 10\(d\) must be) W 300 -14250 M 893.0 0 32 (Huffman\255encoded before transmission to the) W 300 -15350 M 26.7 0 32 (decoder. The first number of the block to be encoded) W 300 -16450 M 541.7 0 32 (is the DC term, which must be differentially) W 300 -17550 M 172.3 0 32 (encoded. If the quantized DC term of the previous) W 300 -18650 M 115.1 0 32 (block is, for example, 12, then the difference is +3.) W 300 -19750 M 234.3 0 32 (Thus, the intermediate representation is \(2\)\(3\), for) W 300 -20850 M (SIZE=2 and AMPLITUDE=3.) h 300 -21950 M 300 -23050 M 46.3 0 32 (Next, the the quantized AC coefficients are encoded.) W 300 -24150 M 488.8 0 32 (Following the zig\255zag order, the first non\255zero) W 300 -25250 M 153.3 0 32 (coefficient is \2552, preceded by a zero\255run of 1. This) W 300 -26350 M 342.4 0 32 (yields an intermediate representation of \(1,2\)\(\2552\).) W 300 -27450 M 371.9 0 32 (Next encountered in the zig\255zag order are three) W 300 -28550 M 174.0 0 32 (consecutive non\255zeros of amplitude \2551. This means) W -7070 42751 T R S 32037 -42745 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 F 1000 o f 200.0 0 32 (each is preceded by a zero\255run of length zero, for) W 300 -2150 M 342.6 0 32 (intermediate symbols \(0,1\)\(\2551\). The last non\255zero) W 300 -3250 M 47.9 0 32 (coefficient is \2551 preceded by two zeros, for \(2,1\)\(\2551\).) W 300 -4350 M 33.6 0 32 (Because this is the last non\255zero coefficient, the final) W 300 -5450 M (symbol representing this 8x8 block is EOB, or \(0,0\).) h 300 -6550 M 300 -7650 M 113.6 0 32 (Thus, the intermediate sequence of symbols for this) W 300 -8750 M (example 8x8 block is: ) h 300 -9850 M 2100 -10950 M (\(2\)\(3\), \(1,2\)\(\2552\), \(0,1\)\(\2551\), \(0,1\)\(\2551\),) h 2100 -12050 M (\(0,1\)\(\2551\), \(2,1\)\(\2551\), \(0,0\)) h 2100 -13150 M 300 -14250 M 19.4 0 32 (Next the codes themselves must be assigned. For this) W 300 -15350 M 498.5 0 32 (example, the VLCs \(Huffman codes\) from the) W 300 -16450 M 534.3 0 32 (informational annex of [2] will be used. The) W 300 -17550 M (differential\255DC VLC for this example is: ) h 300 -18650 M 2100 -19750 M ( \(2\)) h 5744 -19750 M ( 011) h 300 -20850 M 300 -21950 M (The AC luminance VLCs for this example are:) h 300 -23050 M 2100 -24150 M (\(0,0\)) h 5763 -24150 M (1010) h 2100 -25250 M (\(0,1\)) h 5763 -25250 M (00) h 2100 -26350 M (\(1,2\) ) h 5763 -26350 M (11011) h 2100 -27450 M (\(2,1\)) h 5763 -27450 M (11100) h 300 -28550 M -32037 42745 T R S 7094 -5224 T N S 0 -39599 46978 39599 @ R 0 G 300 -1050 M 300 -38493 M S 0 -39599 46978 39599 @ R -7094 5224 T S N S 5226 -42671 50715 36047 @ I N 5226 -6624 T N S 1666 -2062 M /Times-Roman-ISOLatin1 F 800 o f (139) h R S 1666 -3662 M /Times-Roman-ISOLatin1 F 800 o f (144) h R S 1666 -5261 M /Times-Roman-ISOLatin1 F 800 o f (150) h R S 1666 -6778 M /Times-Roman-ISOLatin1 F 800 o f (159) h R S 1666 -8380 M /Times-Roman-ISOLatin1 F 800 o f (159) h R S 1666 -9980 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 1666 -11579 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 1666 -13095 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 3635 -2062 M /Times-Roman-ISOLatin1 F 800 o f (144) h R S 5536 -2062 M /Times-Roman-ISOLatin1 F 800 o f (149) h R S 7438 -2062 M /Times-Roman-ISOLatin1 F 800 o f (153) h R S 9408 -2062 M /Times-Roman-ISOLatin1 F 800 o f (155) h R S 11242 -2062 M /Times-Roman-ISOLatin1 F 800 o f (155) h R S 13143 -2062 M /Times-Roman-ISOLatin1 F 800 o f (155) h R S 15045 -2062 M /Times-Roman-ISOLatin1 F 800 o f (155) h R S 3635 -3662 M /Times-Roman-ISOLatin1 F 800 o f (151) h R S 3635 -5261 M /Times-Roman-ISOLatin1 F 800 o f (155) h R S 3635 -6778 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 3635 -8380 M /Times-Roman-ISOLatin1 F 800 o f (160) h R S 3635 -9980 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 3635 -11579 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 3635 -13095 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 5536 -3750 M /Times-Roman-ISOLatin1 F 800 o f (153) h R S 5536 -5261 M /Times-Roman-ISOLatin1 F 800 o f (160) h R S 5536 -6779 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 5536 -8296 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 5536 -9982 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 5536 -11581 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 5536 -13096 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 7438 -3662 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 7438 -5261 M /Times-Roman-ISOLatin1 F 800 o f (163) h R S 7438 -6779 M /Times-Roman-ISOLatin1 F 800 o f (160) h R S 7438 -8381 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 7438 -9898 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 7438 -11581 M /Times-Roman-ISOLatin1 F 800 o f (163) h R S 7438 -13096 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 9408 -3662 M /Times-Roman-ISOLatin1 F 800 o f (159) h R S 9408 -5262 M /Times-Roman-ISOLatin1 F 800 o f (158) h R S 9408 -6779 M /Times-Roman-ISOLatin1 F 800 o f (160) h R S 9408 -8381 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 9408 -9982 M /Times-Roman-ISOLatin1 F 800 o f (160) h R S 9408 -11581 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 9408 -13096 M /Times-Roman-ISOLatin1 F 800 o f (163) h R S 11242 -3662 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 11242 -5262 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 11242 -6781 M /Times-Roman-ISOLatin1 F 800 o f (159) h R S 11242 -8381 M /Times-Roman-ISOLatin1 F 800 o f (155) h R S 11242 -9982 M /Times-Roman-ISOLatin1 F 800 o f (157) h R S 11242 -11582 M /Times-Roman-ISOLatin1 F 800 o f (157) h R S 11242 -13013 M /Times-Roman-ISOLatin1 F 800 o f (158) h R S 13143 -3662 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 13143 -5262 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 13143 -6779 M /Times-Roman-ISOLatin1 F 800 o f (159) h R S 13143 -8381 M /Times-Roman-ISOLatin1 F 800 o f (155) h R S 13143 -9981 M /Times-Roman-ISOLatin1 F 800 o f (157) h R S 13143 -11581 M /Times-Roman-ISOLatin1 F 800 o f (157) h R S 13143 -13096 M /Times-Roman-ISOLatin1 F 800 o f (158) h R S 15045 -3662 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 15045 -5261 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 15045 -6778 M /Times-Roman-ISOLatin1 F 800 o f (159) h R S 15045 -8294 M /Times-Roman-ISOLatin1 F 800 o f (155) h R S 15045 -9980 M /Times-Roman-ISOLatin1 F 800 o f (157) h R S 15045 -11579 M /Times-Roman-ISOLatin1 F 800 o f (157) h R S 15045 -13095 M /Times-Roman-ISOLatin1 F 800 o f (158) h R S 17966 -2062 M /Times-Roman-ISOLatin1 F 800 o f (235.6) h R S 18093 -3662 M /Times-Roman-ISOLatin1 F 800 o f (\25522.6) h R S 18093 -5261 M /Times-Roman-ISOLatin1 F 800 o f (\25510.9) h R S 18541 -6778 M /Times-Roman-ISOLatin1 F 800 o f (\2557.1) h R S 18541 -8380 M /Times-Roman-ISOLatin1 F 800 o f (\2550.6) h R S 18796 -9980 M /Times-Roman-ISOLatin1 F 800 o f (1.8) h R S 18605 -11579 M /Times-Roman-ISOLatin1 F 800 o f (\2551.3) h R S 18541 -13095 M /Times-Roman-ISOLatin1 F 800 o f (\2552.6) h R S 20446 -2062 M /Times-Roman-ISOLatin1 F 800 o f (\2551.0) h R S 21901 -2062 M /Times-Roman-ISOLatin1 F 800 o f (\25512.1) h R S 24058 -2062 M /Times-Roman-ISOLatin1 F 800 o f (\2555.2) h R S 26156 -2062 M /Times-Roman-ISOLatin1 F 800 o f (2.1) h R S 27669 -2062 M /Times-Roman-ISOLatin1 F 800 o f (\2551.7) h R S 29443 -2062 M /Times-Roman-ISOLatin1 F 800 o f (\2552.7) h R S 31473 -2062 M /Times-Roman-ISOLatin1 F 800 o f (1.3) h R S 19999 -3662 M /Times-Roman-ISOLatin1 F 800 o f (\25517.5) h R S 20446 -5261 M /Times-Roman-ISOLatin1 F 800 o f (\2559.3) h R S 20446 -6778 M /Times-Roman-ISOLatin1 F 800 o f (\2551.9) h R S 20446 -8380 M /Times-Roman-ISOLatin1 F 800 o f (\2550.8) h R S 20446 -9980 M /Times-Roman-ISOLatin1 F 800 o f (\2550.2) h R S 20446 -11579 M /Times-Roman-ISOLatin1 F 800 o f (\2550.4) h R S 20702 -13095 M /Times-Roman-ISOLatin1 F 800 o f (1.6) h R S 22284 -3750 M /Times-Roman-ISOLatin1 F 800 o f (\2556.2) h R S 22284 -5261 M /Times-Roman-ISOLatin1 F 800 o f (\2551.6) h R S 22540 -6779 M /Times-Roman-ISOLatin1 F 800 o f (0.2) h R S 22539 -8296 M /Times-Roman-ISOLatin1 F 800 o f (1.5) h R S 22540 -9982 M /Times-Roman-ISOLatin1 F 800 o f (1.6) h R S 22284 -11581 M /Times-Roman-ISOLatin1 F 800 o f (\2550.3) h R S 22284 -13096 M /Times-Roman-ISOLatin1 F 800 o f (\2553.8) h R S 24058 -3662 M /Times-Roman-ISOLatin1 F 800 o f (\2553.2) h R S 24314 -5261 M /Times-Roman-ISOLatin1 F 800 o f (1.5) h R S 24314 -6779 M /Times-Roman-ISOLatin1 F 800 o f (1.5) h R S 24314 -8381 M /Times-Roman-ISOLatin1 F 800 o f (1.6) h R S 24058 -9898 M /Times-Roman-ISOLatin1 F 800 o f (\2550.3) h R S 24058 -11581 M /Times-Roman-ISOLatin1 F 800 o f (\2551.5) h R S 24058 -13096 M /Times-Roman-ISOLatin1 F 800 o f (\2551.8) h R S 25836 -3662 M /Times-Roman-ISOLatin1 F 800 o f (\2552.9) h R S 26092 -5262 M /Times-Roman-ISOLatin1 F 800 o f (0.2) h R S 26156 -6779 M /Times-Roman-ISOLatin1 F 800 o f (0.9) h R S 25836 -8381 M /Times-Roman-ISOLatin1 F 800 o f (\2550.1) h R S 25836 -9982 M /Times-Roman-ISOLatin1 F 800 o f (\2550.8) h R S 25836 -11581 M /Times-Roman-ISOLatin1 F 800 o f (\2550.5) h R S 26156 -13096 M /Times-Roman-ISOLatin1 F 800 o f (1.9) h R S 27669 -3662 M /Times-Roman-ISOLatin1 F 800 o f (\2550.1) h R S 27670 -5262 M /Times-Roman-ISOLatin1 F 800 o f (\2550.9) h R S 27670 -6781 M /Times-Roman-ISOLatin1 F 800 o f (\2550.1) h R S 27669 -8381 M /Times-Roman-ISOLatin1 F 800 o f (\2550.7) h R S 27925 -9982 M /Times-Roman-ISOLatin1 F 800 o f (1.5) h R S 27925 -11582 M /Times-Roman-ISOLatin1 F 800 o f (1.7) h R S 27925 -13013 M /Times-Roman-ISOLatin1 F 800 o f (1.2) h R S 29699 -3662 M /Times-Roman-ISOLatin1 F 800 o f (0.4) h R S 29443 -5262 M /Times-Roman-ISOLatin1 F 800 o f (\2550.6) h R S 29699 -6779 M /Times-Roman-ISOLatin1 F 800 o f (0.0) h R S 29699 -8381 M /Times-Roman-ISOLatin1 F 800 o f (0.6) h R S 29699 -9981 M /Times-Roman-ISOLatin1 F 800 o f (1.0) h R S 29699 -11581 M /Times-Roman-ISOLatin1 F 800 o f (1.1) h R S 29443 -13096 M /Times-Roman-ISOLatin1 F 800 o f (\2550.6) h R S 31218 -3662 M /Times-Roman-ISOLatin1 F 800 o f (\2551.2) h R S 31218 -5261 M /Times-Roman-ISOLatin1 F 800 o f (\2550.1) h R S 31473 -6778 M /Times-Roman-ISOLatin1 F 800 o f (0.3) h R S 31473 -8294 M /Times-Roman-ISOLatin1 F 800 o f (1.3) h R S 31217 -9980 M /Times-Roman-ISOLatin1 F 800 o f (\2551.0) h R S 31218 -11579 M /Times-Roman-ISOLatin1 F 800 o f (\2550.8) h R S 31218 -13095 M /Times-Roman-ISOLatin1 F 800 o f (\2550.4) h R S 3031 -15447 M /Times-Roman-ISOLatin1 F 1000 o f (\(a\) source image samples) h R S 19330 -15381 M /Times-Roman-ISOLatin1 F 1000 o f (\(b\) forward DCT coefficients) h R S 34456 -2062 M /Times-Roman-ISOLatin1 F 800 o f (16) h R S 34456 -3662 M /Times-Roman-ISOLatin1 F 800 o f (12) h R S 34456 -5261 M /Times-Roman-ISOLatin1 F 800 o f (14) h R S 34456 -6778 M /Times-Roman-ISOLatin1 F 800 o f (14) h R S 34456 -8380 M /Times-Roman-ISOLatin1 F 800 o f (18) h R S 34456 -9980 M /Times-Roman-ISOLatin1 F 800 o f (24) h R S 34456 -11579 M /Times-Roman-ISOLatin1 F 800 o f (49) h R S 34456 -13095 M /Times-Roman-ISOLatin1 F 800 o f (72) h R S 36425 -2062 M /Times-Roman-ISOLatin1 F 800 o f (11) h R S 38326 -2062 M /Times-Roman-ISOLatin1 F 800 o f (10) h R S 40228 -2062 M /Times-Roman-ISOLatin1 F 800 o f (16) h R S 42198 -2062 M /Times-Roman-ISOLatin1 F 800 o f (24) h R S 44032 -2062 M /Times-Roman-ISOLatin1 F 800 o f (40) h R S 45933 -2062 M /Times-Roman-ISOLatin1 F 800 o f (51) h R S 47835 -2062 M /Times-Roman-ISOLatin1 F 800 o f (61) h R S 36425 -3662 M /Times-Roman-ISOLatin1 F 800 o f (12) h R S 36425 -5261 M /Times-Roman-ISOLatin1 F 800 o f (13) h R S 36425 -6778 M /Times-Roman-ISOLatin1 F 800 o f (17) h R S 36425 -8380 M /Times-Roman-ISOLatin1 F 800 o f (22) h R S 36425 -9980 M /Times-Roman-ISOLatin1 F 800 o f (35) h R S 36425 -11579 M /Times-Roman-ISOLatin1 F 800 o f (64) h R S 36425 -13095 M /Times-Roman-ISOLatin1 F 800 o f (92) h R S 38326 -3750 M /Times-Roman-ISOLatin1 F 800 o f (14) h R S 38326 -5261 M /Times-Roman-ISOLatin1 F 800 o f (16) h R S 38326 -6779 M /Times-Roman-ISOLatin1 F 800 o f (22) h R S 38326 -8296 M /Times-Roman-ISOLatin1 F 800 o f (37) h R S 38326 -9982 M /Times-Roman-ISOLatin1 F 800 o f (55) h R S 38326 -11581 M /Times-Roman-ISOLatin1 F 800 o f (78) h R S 38326 -13096 M /Times-Roman-ISOLatin1 F 800 o f (95) h R S 40228 -3662 M /Times-Roman-ISOLatin1 F 800 o f (19) h R S 40228 -5261 M /Times-Roman-ISOLatin1 F 800 o f (24) h R S 40228 -6779 M /Times-Roman-ISOLatin1 F 800 o f (29) h R S 40228 -8381 M /Times-Roman-ISOLatin1 F 800 o f (56) h R S 40228 -9898 M /Times-Roman-ISOLatin1 F 800 o f (64) h R S 40228 -11581 M /Times-Roman-ISOLatin1 F 800 o f (87) h R S 40228 -13096 M /Times-Roman-ISOLatin1 F 800 o f (98) h R S 42198 -3662 M /Times-Roman-ISOLatin1 F 800 o f (26) h R S 42198 -5262 M /Times-Roman-ISOLatin1 F 800 o f (40) h R S 42198 -6779 M /Times-Roman-ISOLatin1 F 800 o f (51) h R S 42198 -8381 M /Times-Roman-ISOLatin1 F 800 o f (68) h R S 42198 -9982 M /Times-Roman-ISOLatin1 F 800 o f (81) h R S 42198 -11581 M /Times-Roman-ISOLatin1 F 800 o f (103) h R S 42198 -13096 M /Times-Roman-ISOLatin1 F 800 o f (112) h R S 44032 -3662 M /Times-Roman-ISOLatin1 F 800 o f (58) h R S 44032 -5262 M /Times-Roman-ISOLatin1 F 800 o f (57) h R S 44032 -6781 M /Times-Roman-ISOLatin1 F 800 o f (87) h R S 44032 -8381 M /Times-Roman-ISOLatin1 F 800 o f (109) h R S 44032 -9982 M /Times-Roman-ISOLatin1 F 800 o f (104) h R S 44032 -11582 M /Times-Roman-ISOLatin1 F 800 o f (121) h R S 44032 -13013 M /Times-Roman-ISOLatin1 F 800 o f (100) h R S 45933 -3662 M /Times-Roman-ISOLatin1 F 800 o f (60) h R S 45933 -5262 M /Times-Roman-ISOLatin1 F 800 o f (69) h R S 45933 -6779 M /Times-Roman-ISOLatin1 F 800 o f (80) h R S 45933 -8381 M /Times-Roman-ISOLatin1 F 800 o f (103) h R S 45933 -9981 M /Times-Roman-ISOLatin1 F 800 o f (113) h R S 45933 -11581 M /Times-Roman-ISOLatin1 F 800 o f (120) h R S 45933 -13096 M /Times-Roman-ISOLatin1 F 800 o f (103) h R S 47835 -3662 M /Times-Roman-ISOLatin1 F 800 o f (55) h R S 47835 -5261 M /Times-Roman-ISOLatin1 F 800 o f (56) h R S 47835 -6778 M /Times-Roman-ISOLatin1 F 800 o f (62) h R S 47835 -8294 M /Times-Roman-ISOLatin1 F 800 o f (77) h R S 47835 -9980 M /Times-Roman-ISOLatin1 F 800 o f (92) h R S 47835 -11579 M /Times-Roman-ISOLatin1 F 800 o f (101) h R S 47835 -13095 M /Times-Roman-ISOLatin1 F 800 o f (99) h R S 37419 -15381 M /Times-Roman-ISOLatin1 F 1000 o f (\(c\) quantization table) h R S 1668 -18096 M /Times-Roman-ISOLatin1 F 798 o f (15) h R S 1668 -19695 M /Times-Roman-ISOLatin1 F 796 o f (\2552) h R S 1668 -21296 M /Times-Roman-ISOLatin1 F 796 o f (\2551) h R S 1858 -22812 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 1858 -24412 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 1858 -26013 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 1858 -27613 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 1858 -29130 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 3827 -18096 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 5536 -18096 M /Times-Roman-ISOLatin1 F 800 o f (\2551) h R S 7630 -18096 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 9600 -18096 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 11434 -18096 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 13335 -18096 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 15237 -18096 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 3635 -19695 M /Times-Roman-ISOLatin1 F 800 o f (\2551) h R S 3635 -21296 M /Times-Roman-ISOLatin1 F 800 o f (\2551) h R S 3827 -22812 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 3827 -24412 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 3827 -26013 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 3827 -27613 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 3827 -29130 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 5728 -19781 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 5728 -21296 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 5728 -22813 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 5728 -24330 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 5728 -26015 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 5728 -27614 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 5728 -29131 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 7630 -19695 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 7630 -21296 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 7630 -22813 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 7630 -24413 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 7630 -25928 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 7630 -27614 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 7630 -29131 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 9600 -19695 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 9600 -21297 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 9600 -22813 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 9600 -24413 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 9600 -26015 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 9600 -27614 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 9600 -29131 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 11434 -19695 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 11434 -21297 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 11434 -22814 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 11434 -24413 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 11434 -26015 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 11434 -27615 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 11434 -29045 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 13335 -19695 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 13335 -21297 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 13335 -22813 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 13335 -24413 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 13335 -26014 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 13335 -27614 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 13335 -29131 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 15237 -19695 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 15237 -21296 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 15237 -22812 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 15237 -24329 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 15237 -26013 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 15237 -27613 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 15237 -29130 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 3927 -31436 M /Times-Roman-ISOLatin1 F 1000 o f (\(d\) normalized quantized) h R S 19139 -31500 M /Times-Roman-ISOLatin1 F 1000 o f (\(e\) denormalized quantized) h R S 34201 -18169 M /Times-Roman-ISOLatin1 F 800 o f (144) h R S 34201 -19770 M /Times-Roman-ISOLatin1 F 800 o f (148) h R S 34201 -21372 M /Times-Roman-ISOLatin1 F 800 o f (155) h R S 34201 -22887 M /Times-Roman-ISOLatin1 F 800 o f (160) h R S 34201 -24488 M /Times-Roman-ISOLatin1 F 800 o f (163) h R S 34201 -26088 M /Times-Roman-ISOLatin1 F 800 o f (163) h R S 34201 -27688 M /Times-Roman-ISOLatin1 F 800 o f (160) h R S 34201 -29204 M /Times-Roman-ISOLatin1 F 800 o f (158) h R S 36170 -18169 M /Times-Roman-ISOLatin1 F 800 o f (146) h R S 38071 -18169 M /Times-Roman-ISOLatin1 F 800 o f (149) h R S 39973 -18169 M /Times-Roman-ISOLatin1 F 800 o f (152) h R S 41943 -18169 M /Times-Roman-ISOLatin1 F 800 o f (154) h R S 43777 -18169 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 45678 -18169 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 47580 -18169 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 36170 -19770 M /Times-Roman-ISOLatin1 F 800 o f (150) h R S 36170 -21372 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 36170 -22887 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 36170 -24488 M /Times-Roman-ISOLatin1 F 800 o f (163) h R S 36170 -26088 M /Times-Roman-ISOLatin1 F 800 o f (164) h R S 36170 -27688 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 36170 -29204 M /Times-Roman-ISOLatin1 F 800 o f (159) h R S 38071 -19856 M /Times-Roman-ISOLatin1 F 800 o f (152) h R S 38071 -21372 M /Times-Roman-ISOLatin1 F 800 o f (157) h R S 38071 -22888 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 38071 -24405 M /Times-Roman-ISOLatin1 F 800 o f (164) h R S 38071 -26090 M /Times-Roman-ISOLatin1 F 800 o f (164) h R S 38071 -27689 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 38071 -29206 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 39973 -19770 M /Times-Roman-ISOLatin1 F 800 o f (154) h R S 39973 -21372 M /Times-Roman-ISOLatin1 F 800 o f (158) h R S 39973 -22888 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 39973 -24489 M /Times-Roman-ISOLatin1 F 800 o f (163) h R S 39973 -26003 M /Times-Roman-ISOLatin1 F 800 o f (164) h R S 39973 -27689 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 39973 -29206 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 41943 -19770 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 41943 -21373 M /Times-Roman-ISOLatin1 F 800 o f (158) h R S 41943 -22888 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 41943 -24489 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 41943 -26090 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 41943 -27689 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 41943 -29206 M /Times-Roman-ISOLatin1 F 800 o f (162) h R S 43777 -19770 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 43777 -21373 M /Times-Roman-ISOLatin1 F 800 o f (157) h R S 43777 -22889 M /Times-Roman-ISOLatin1 F 800 o f (159) h R S 43777 -24489 M /Times-Roman-ISOLatin1 F 800 o f (160) h R S 43777 -26090 M /Times-Roman-ISOLatin1 F 800 o f (160) h R S 43777 -27690 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 43777 -29122 M /Times-Roman-ISOLatin1 F 800 o f (161) h R S 45678 -19770 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 45678 -21373 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 45678 -22888 M /Times-Roman-ISOLatin1 F 800 o f (157) h R S 45678 -24489 M /Times-Roman-ISOLatin1 F 800 o f (158) h R S 45678 -26089 M /Times-Roman-ISOLatin1 F 800 o f (158) h R S 45678 -27689 M /Times-Roman-ISOLatin1 F 800 o f (159) h R S 45678 -29206 M /Times-Roman-ISOLatin1 F 800 o f (159) h R S 47580 -19770 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 47580 -21372 M /Times-Roman-ISOLatin1 F 800 o f (155) h R S 47580 -22887 M /Times-Roman-ISOLatin1 F 800 o f (155) h R S 47580 -24402 M /Times-Roman-ISOLatin1 F 800 o f (156) h R S 47580 -26088 M /Times-Roman-ISOLatin1 F 800 o f (157) h R S 47580 -27688 M /Times-Roman-ISOLatin1 F 800 o f (158) h R S 47580 -29204 M /Times-Roman-ISOLatin1 F 800 o f (158) h R S 34861 -31630 M /Times-Roman-ISOLatin1 F 1000 o f (\(f\) reconstructed image samples) h R S 16167 -34835 M /Times-Roman-ISOLatin1 F 1000 o f (Figure 10. DCT and Quantization Examples) h R S 17704 -17741 M /Times-Roman-ISOLatin1 F 800 o f (240) h R S 17703 -19304 M /Times-Roman-ISOLatin1 F 800 o f (\25524) h R S 17703 -20869 M /Times-Roman-ISOLatin1 F 800 o f (\25514) h R S 18087 -22350 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 18087 -23914 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 18087 -25479 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 18087 -27042 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 18087 -28525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 20056 -17741 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 21573 -17741 M /Times-Roman-ISOLatin1 F 800 o f (\25510) h R S 23859 -17741 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 25829 -17741 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 27663 -17741 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 29564 -17741 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 31466 -17741 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 19672 -19304 M /Times-Roman-ISOLatin1 F 800 o f (\25512) h R S 19672 -20869 M /Times-Roman-ISOLatin1 F 800 o f (\25513) h R S 20056 -22350 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 20056 -23914 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 20056 -25479 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 20056 -27042 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 20056 -28525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 21957 -19388 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 21957 -20869 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 21957 -22351 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 21957 -23833 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 21957 -25481 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 21957 -27043 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 21957 -28526 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 23859 -19304 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 23859 -20869 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 23859 -22351 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 23859 -23915 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 23859 -25396 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 23859 -27043 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 23859 -28526 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 25829 -19304 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 25829 -20870 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 25829 -22351 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 25829 -23915 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 25829 -25481 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 25829 -27043 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 25829 -28526 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 27663 -19304 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 27663 -20870 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 27663 -22352 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 27663 -23915 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 27663 -25481 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 27663 -27044 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 27663 -28443 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 29564 -19304 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 29564 -20870 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 29564 -22351 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 29564 -23915 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 29564 -25480 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 29564 -27043 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 29564 -28526 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 31466 -19304 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 31466 -20869 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 31466 -22350 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 31466 -23832 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 31466 -25479 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 31466 -27042 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 31466 -28525 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 5462 -32484 M /Times-Roman-ISOLatin1 F 1000 o f (coefficients) h R S 20706 -32581 M /Times-Roman-ISOLatin1 F 1000 o f (coefficients) h R R R R S 30200 -75546 M /Times-Roman-ISOLatin1 F 1000 o f (12) h R showpage $P e %%Page: 13 13 /$P a D g N 0 79200 T S S 7200 -2700 T N 0 G 300 -1200 M -7200 2700 T R S 7200 -74700 T N 0 G 300 -1200 M -7200 74700 T R R S 7172 -7467 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 153.2 0 32 (The VLIs specified in [2] are related to the two's) W 300 -2150 M (complement representation. They are:) h 300 -3250 M 2100 -4350 M (\(3\)) h 5739 -4350 M (11) h 2100 -5450 M (\(\2552\)) h 5739 -5450 M (01) h 2100 -6550 M (\(\2551\) ) h 5739 -6550 M (0) h 300 -7650 M 300 -8750 M 40.2 0 32 (Thus, the bit\255stream for this 8x8 example block is as) W 300 -9850 M 108.3 0 32 (follows. Note that 31 bits are required to represent) W 300 -10950 M 120.8 0 32 (64 coefficients, which achieves compression of just) W 300 -12050 M (under 0.5 bits/sample:) h 300 -13150 M 2100 -14250 M ( 0111111011010000000001110001010 ) h 2100 -15350 M 300 -16450 M 300 -17550 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1000 o f (7.4 Other DCT Sequential Codecs) h 300 -18650 M 300 -19750 M /Times-Roman-ISOLatin1 F 1000 o f 246.4 0 32 (The structure of the 12\255bit DCT sequential codec) W 300 -20850 M 106.8 0 32 (with Huffman coding is a straightforward extension) W 300 -21950 M 120.7 0 32 (of the entropy coding method described previously.) W 300 -23050 M 104.6 0 32 (Quantized DCT coefficients can be 4 bits larger, so) W 300 -24150 M 433.6 0 32 (the SIZE and AMPLITUDE information extend) W 300 -25250 M 46.5 0 32 (accordingly. DCT sequential with arithmetic coding) W 300 -26350 M (is described in detail in [2].) h 300 -27450 M 300 -28550 M 300 -29800 M /Times-Bold-ISOLatin1 F 1200 o f (8 DCT Progressive Mode) h 300 -31550 M /Times-Roman-ISOLatin1 F 1000 o f 87.6 0 32 (The DCT progressive mode of operation consists of) W 300 -32650 M 8.1 0 32 (the same FDCT and Quantization steps \(from section) W 300 -33750 M 94.7 0 32 (4\) that are used by DCT sequential mode. The key) W 300 -34850 M 95.9 0 32 (difference is that each image component is encoded) W 300 -35950 M 133.5 0 32 (in multiple scans rather than in a single scan. The) W 300 -37050 M 32.4 0 32 (first scan\(s\) encode a rough but recognizable version) W 300 -38150 M 225.9 0 32 (of the image which can be transmitted quickly in) W 300 -39250 M 202.4 0 32 (comparison to the total transmission time, and are) W 300 -40350 M 52.6 0 32 (refined by succeeding scans until reaching a level of) W 300 -41450 M 764.0 0 32 (picture quality that was established by the) W 300 -42550 M (quantization tables.) h 300 -43650 M 300 -44750 M 643.1 0 32 (To achieve this requires the addition of an) W 300 -45850 M 349.6 0 32 (image\255sized buffer memory at the output of the) W 300 -46950 M 94.3 0 32 (quantizer, before the input to entropy encoder. The) W 300 -48050 M 37.3 0 32 (buffer memory must be of sufficient size to store the) W 300 -49150 M 60.1 0 32 (image as quantized DCT coefficients, each of which) W 300 -50250 M 101.0 0 32 (\(if stored straightforwardly\) is 3 bits larger than the) W 300 -51350 M 229.6 0 32 (source image samples. After each block of DCT) W 300 -52450 M 639.0 0 32 (coefficients is quantized, it is stored in the) W 300 -53550 M 40.2 0 32 (coefficient buffer memory. The buffered coefficients) W 300 -54650 M (are then partially encoded in each of multiple scans.) h 300 -55750 M 300 -56850 M 151.3 0 32 (There are two complementary methods by which a) W 300 -57950 M 0.4 0 32 (block of quantized DCT coefficients may be partially) W 300 -59050 M 635.3 0 32 (encoded. First, only a specified ) W 635.3 0 32 (\026) W 635.3 0 32 (band) W 635.3 0 32 (\027) W 635.3 0 32 ( of) W 300 -60150 M 431.5 0 32 (coefficients from the zig\255zag sequence need be) W 300 -61250 M 292.0 0 32 (encoded within a given scan. This procedure is) W 300 -62350 M 595.6 0 32 (called ) W 595.6 0 32 (\026) W 595.6 0 32 (spectral selection,) W 595.6 0 32 (\027) W 595.6 0 32 ( because each band) W 300 -63450 M 51.5 0 32 (typically contains coefficients which occupy a lower) W -7172 7467 T R S 32040 -7170 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 F 1000 o f 119.7 0 32 (or higher part of the spatial\255frequency spectrum for) W 300 -2150 M 31.4 0 32 (that 8x8 block. Secondly, the coefficients within the) W 300 -3250 M 392.8 0 32 (current band need not be encoded to their full) W 300 -4350 M 389.5 0 32 (\(quantized\) accuracy in a given scan. Upon a) W 300 -5450 M 204.0 0 32 (coefficient's first encoding, the N most significant) W 300 -6550 M 64.3 0 32 (bits can be encoded first, where N is specifiable. In) W 300 -7650 M 7.1 0 32 (subsequent scans, the less significant bits can then be) W 300 -8750 M 426.7 0 32 (encoded. This procedure is called ``successive) W 300 -9850 M 435.7 0 32 (approximation.'' Both procedures can be used) W 300 -10950 M (separately, or mixed in flexible combinations.) h 300 -12050 M 300 -30888 M /Times-Roman-ISOLatin1 F 1000 o f 116.0 0 32 (Some intuition for spectral selection and successive) W 300 -31988 M 48.9 0 32 (approximation can be obtained from Figure 11. The) W 300 -33088 M 578.4 0 32 (quantized DCT coefficient information can be) W 300 -34188 M 247.6 0 32 (viewed as a rectangle for which the axes are the) W 300 -35288 M 570.2 0 32 (DCT coefficients \(in zig\255zag order\) and their) W 300 -36388 M 37.2 0 32 (amplitudes. Spectral selection slices the information) W 300 -37488 M 199.2 0 32 (in one dimension and successive approximation in) W 300 -38588 M (the other.) h 300 -39688 M 300 -40788 M 300 -42038 M /Times-Bold-ISOLatin1 F 1200 o f (9 Hierarchical Mode of Operation) h 300 -43788 M /Times-Roman-ISOLatin1 F 1000 o f 556.4 0 32 (The hierarchical mode provides a ) W 556.4 0 32 (\026) W 556.4 0 32 (pyramidal) W 556.4 0 32 (\027) W 300 -44888 M 170.9 0 32 (encoding of an image at multiple resolutions, each) W 300 -45988 M 63.7 0 32 (differing in resolution from its adjacent encoding by) W 300 -47088 M 204.1 0 32 (a factor of two in either the horizontal or vertical) W 300 -48188 M 97.6 0 32 (dimension or both. The encoding procedure can be) W 300 -49288 M (summarized as follows:) h 300 -50388 M 300 -51488 M (1\)) h 2100 -51488 M 214.0 0 32 (Filter and down\255sample the original image by) W 2100 -52588 M 237.0 0 32 (the desired number of multiples of 2 in each) W 2100 -53688 M (dimension.) h 2100 -54788 M 300 -55888 M (2\)) h 2100 -55888 M 29.0 0 32 (Encode this reduced\255size image using one of the) W 2100 -56988 M 251.2 0 32 (sequential DCT, progressive DCT, or lossless) W 2100 -58088 M (encoders described previously.) h 2100 -59188 M 300 -60288 M (3\)) h 2100 -60288 M 629.6 0 32 (Decode this reduced\255size image and then) W 2100 -61388 M 214.0 0 32 (interpolate and up\255sample it by 2 horizontally) W 2100 -62488 M 1286.3 0 32 (and/or vertically, using the identical) W 2100 -63588 M (interpolation filter which the receiver must use.) h -32040 7170 T S N S 32282 -37308 21475 17738 @ I N 32282 -19570 T N S 3610 -15064 M /Times-Roman-ISOLatin1 F 1000 o f (Table 3. Baseline Entropy Coding) h R S 7350 -16502 M /Times-Roman-ISOLatin1 F 1000 o f (Symbol\2552 Structure) h R S 4858 -3655 M /Times-Roman-ISOLatin1 F 1100 o f (1) h R S 4858 -4709 M /Times-Roman-ISOLatin1 F 1100 o f (2) h R S 4858 -5764 M /Times-Roman-ISOLatin1 F 1100 o f (3) h R S 4858 -6722 M /Times-Roman-ISOLatin1 F 1100 o f (4) h R S 4858 -7777 M /Times-Roman-ISOLatin1 F 1100 o f (5) h R S 4858 -8832 M /Times-Roman-ISOLatin1 F 1100 o f (6) h R S 4858 -9791 M /Times-Roman-ISOLatin1 F 1100 o f (7) h R S 4858 -10846 M /Times-Roman-ISOLatin1 F 1100 o f (8) h R S 4858 -11804 M /Times-Roman-ISOLatin1 F 1100 o f (9) h R S 4378 -12859 M /Times-Roman-ISOLatin1 F 1100 o f (10) h R S 11665 -3655 M /Times-Roman-ISOLatin1 F 1100 o f (\2551,1) h R S 10610 -4709 M /Times-Roman-ISOLatin1 F 1100 o f (\2553,\2552,2,3) h R S 10418 -5764 M /Times-Roman-ISOLatin1 F 1100 o f (\2557..\2554,4..7) h R S 9843 -6722 M /Times-Roman-ISOLatin1 F 1100 o f (\25515..\2558,8..15) h R S 9268 -7777 M /Times-Roman-ISOLatin1 F 1100 o f (\25531..\25516,16..31) h R S 9268 -8832 M /Times-Roman-ISOLatin1 F 1100 o f (\25563..\25532,32..63) h R S 8692 -9791 M /Times-Roman-ISOLatin1 F 1100 o f (\255127..\25564,64..127) h R S 8214 -10846 M /Times-Roman-ISOLatin1 F 1100 o f (\255255..\255128,128..255) h R S 8214 -11804 M /Times-Roman-ISOLatin1 F 1100 o f (\255511..\255256,256..511) h R S 7638 -12859 M /Times-Roman-ISOLatin1 F 1100 o f (\2551023..\255512,512..1023) h R S 2556 -13507 17736 12745 @ S 50 w 0 c 0 j 2 i 0.00 G k R R S N 2679.00 -2454.00 M 20333.00 -2454.00 L S 50 w 0 c 0 j 2 i 0.00 G k R R S 3889 -2073 M /Times-Roman-ISOLatin1 F 1100 o f (SIZE) h R S 9354 -2073 M /Times-Roman-ISOLatin1 F 1100 o f (AMPLITUDE) h R R R R S 30008 -75738 M /Times-Roman-ISOLatin1 F 1000 o f (13) h R showpage $P e %%Page: 14 14 /$P a D g N 0 79200 T S S 7200 -2700 T N 0 G 300 -1200 M -7200 2700 T R S 7200 -74700 T N 0 G 300 -1200 M -7200 74700 T R R S 7152 -59314 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f (4\)) h 2100 -1050 M 7.9 0 32 (Use this up\255sampled image as a prediction of the) W 2100 -2150 M 505.7 0 32 (original at this resolution, and encode the) W 2100 -3250 M 307.0 0 32 (difference image using one of the sequential) W 2100 -4350 M 351.4 0 32 (DCT, progressive DCT, or lossless encoders) W 2100 -5450 M (described previously.) h 2100 -6550 M 300 -7650 M (5\)) h 2100 -7650 M 16.1 0 32 (Repeat steps 3\) and 4\) until the full resolution of) W 2100 -8750 M (the image has been encoded.) h 2100 -9850 M 300 -10950 M 75.1 0 32 (The encoding in steps 2\) and 4\) must be done using) W 300 -12050 M 144.8 0 32 (only DCT\255based processes, only lossless processes,) W -7152 59314 T R S 32040 -59325 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 F 1000 o f 32.1 0 32 (or DCT\255based processes with a final lossless process) W 300 -2150 M (for each component.) h 300 -3250 M 300 -4350 M 292.0 0 32 (Hierarchical encoding is useful in applications in) W 300 -5450 M 10.8 0 32 (which a very high resolution image must be accessed) W 300 -6550 M 243.3 0 32 (by a lower\255resolution display. An example is an) W 300 -7650 M 16.3 0 32 (image scanned and compressed at high resolution for) W 300 -8750 M 218.6 0 32 (a very high\255quality printer, where the image must) W 300 -9850 M 357.1 0 32 (also be displayed on a low\255resolution PC video) W 300 -10950 M (screen.) h 300 -12050 M -32040 59325 T R S 7478 -5752 T N S 0 -55990 47170 55990 @ R 0 G 300 -1050 M 300 -55560 M S 0 -55990 47170 55990 @ R -7478 5752 T S N S 7910 -60266 46306 53114 @ I N 7910 -7152 T N S N 28051.00 -26485.00 M 29810.00 -26485.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 29355.00 -26739.00 M 29899.00 -26485.00 L 29355.00 -26232.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 27572 -26841 1434 854 @ S 0.00 G - + * E R R S N 7951.00 -5609.00 M 7951.00 -7452.00 L S 150 w 0 c 0 j [100 400] 0 d 0.00 G k R R S N 10071.00 -2868.00 M 12373.00 -2107.00 L S 150 w 0 c 0 j [100 400] 0 d 0.00 G k R R S 27673 -24959 2034 3299 @ S 0.00 G - + * E R S 100 w 0 c 0 j 2 i 0.00 G k R R S N 28111.00 -24989.00 M 28111.00 -21690.00 L 34561.00 -16951.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 28586.00 -24989.00 M 28586.00 -21690.00 L 35034.00 -16951.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 29170.00 -24989.00 M 29170.00 -21713.00 L 35515.00 -17004.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 27752.00 -21655.00 M 34156.00 -16950.00 L 36061.00 -17005.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 29765.00 -24993.00 M 36112.00 -19542.00 L 36112.00 -17114.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 27936 -34013 657 3168 @ S 0.00 G - + * E R S 100 w 0 c 0 j 2 i 0.00 G k R R S N 28014.00 -30789.00 M 34616.00 -26319.00 L 35158.00 -26319.00 L 28609.00 -30789.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 35159.00 -26369.00 M 35159.00 -29208.00 L 28598.00 -34045.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 28070.00 -21382.00 M 30187.00 -21382.00 L 30187.00 -24611.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 28491.00 -21051.00 M 30609.00 -21051.00 L 30609.00 -24282.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 29073.00 -33616.00 M 29073.00 -30462.00 L 28491.00 -30462.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 29496.00 -33297.00 M 29496.00 -30145.00 L 28915.00 -30145.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 31982.00 -21620.00 M 33692.00 -20185.00 L S 150 w 0 c 0 j [100 400] 0 d 0.00 G k R R S N 31469.00 -29792.00 M 33236.00 -28348.00 L S 150 w 0 c 0 j [100 400] 0 d 0.00 G k R R S 28254 -45069 659 3261 @ S 0.00 G - + * E R S 100 w 0 c 0 j 2 i 0.00 G k R R S N 28333.00 -41749.00 M 34935.00 -37152.00 L 35477.00 -37152.00 L 28927.00 -41749.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 35477.00 -37203.00 M 35477.00 -40126.00 L 28915.00 -45102.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 29337.00 -44777.00 M 29337.00 -41405.00 L 28861.00 -41405.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 29707.00 -44452.00 M 29707.00 -41205.00 L 29231.00 -41205.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 31527.00 -41856.00 M 33350.00 -40419.00 L S 150 w 0 c 0 j [100 400] 0 d 0.00 G k R R S 6408 -35969 4044 1320 @ S 0.00 G - + * E R S 100 w 0 c 0 j 2 i 0.00 G k R R S N 6459.00 -34679.00 M 13019.00 -30105.00 L 16445.00 -30105.00 L 10505.00 -34652.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 6901.00 -34370.00 M 10756.00 -34370.00 L 10756.00 -35713.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 7363.00 -34064.00 M 11218.00 -34064.00 L 11218.00 -35455.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 16436.00 -30163.00 M 16436.00 -31362.00 L 10508.00 -35947.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 6487.00 -35060.00 M 10508.00 -35060.00 L 16488.00 -30526.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 6487.00 -35530.00 M 10508.00 -35530.00 L 16488.00 -30994.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 8585 -1604 M /Times-Roman-ISOLatin1 F 800 o f (Blocks) h R S 4074 -6206 M /Times-Roman-ISOLatin1 F 800 o f (DCT) h R S 3023 -6976 M /Times-Roman-ISOLatin1 F 800 o f (coefficients) h R S 16940 -8844 M /Times-Roman-ISOLatin1 F 1000 o f (\(a\) image component) h R S 18710 -9709 M /Times-Roman-ISOLatin1 F 1000 o f (as quantized) h R S 17936 -10669 M /Times-Roman-ISOLatin1 F 1000 o f (DCT coefficients) h R S 27584 -26840 M /Times-Roman-ISOLatin1 F 800 o f (MSB) h R S 27853 -28363 M /Times-Roman-ISOLatin1 F 800 o f (2) h 0.0 358.0 m (nd) h 0 -358.0 m ( scan) h R S 6859 -20758 M /Times-Roman-ISOLatin1 F 800 o f (1) h 0.0 358.0 m (st) h 0 -358.0 m ( scan) h R S 6408 -45081 4044 1293 @ S 0.00 G - + * E R S 100 w 0 c 0 j 2 i 0.00 G k R R S N 6459.00 -43816.00 M 13019.00 -39334.00 L 16445.00 -39334.00 L 10505.00 -43791.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 6901.00 -43493.00 M 10803.00 -43493.00 L 10803.00 -44709.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 7476.00 -43156.00 M 11377.00 -43156.00 L 11377.00 -44424.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 10870.00 -42266.00 M 12410.00 -40955.00 L S 150 w 0 c 0 j [100 400] 0 d 0.00 G k R R S N 16436.00 -39388.00 M 16436.00 -40562.00 L 10508.00 -45061.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 6487.00 -44192.00 M 10508.00 -44192.00 L 16488.00 -39744.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 6487.00 -44650.00 M 10508.00 -44650.00 L 16488.00 -40203.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 6533 -37579 M /Times-Roman-ISOLatin1 F 800 o f (3) h 0.0 358.0 m (rd) h 0 -358.0 m ( scan) h R S 27519 -36504 M /Times-Roman-ISOLatin1 F 800 o f (3) h 0.0 358.0 m (rd) h 0 -358.0 m ( scan) h R S 27906 -46729 M /Times-Roman-ISOLatin1 F 800 o f (\(LSB\)) h R S 27906 -47951 M /Times-Roman-ISOLatin1 F 800 o f (6) h 0.0 358.0 m (th) h 0 -358.0 m ( scan) h R S 32477 -24147 M /Times-Roman-ISOLatin1 F 800 o f (sending) h R S 14094 -34924 M /Times-Roman-ISOLatin1 F 800 o f (sending) h R S 14011 -43670 M /Times-Roman-ISOLatin1 F 800 o f (sending) h R S 32059 -44171 M /Times-Roman-ISOLatin1 F 800 o f (sending) h R S 31912 -32940 M /Times-Roman-ISOLatin1 F 800 o f (sending) h R S N 10629.00 -10527.00 M 11896.00 -10527.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 11441.00 -10781.00 M 11985.00 -10527.00 L 11441.00 -10274.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 31350.00 -24176.00 M 33120.00 -22714.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 32930.00 -23199.00 M 33188.00 -22658.00 L 32607.00 -22808.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 30555.00 -33224.00 M 32324.00 -31762.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 32135.00 -32247.00 M 32392.00 -31706.00 L 31811.00 -31857.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 30662.00 -44524.00 M 32429.00 -43059.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 32240.00 -43545.00 M 32497.00 -43003.00 L 31917.00 -43155.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 12784.00 -43931.00 M 14621.00 -42531.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 14413.00 -43008.00 M 14692.00 -42477.00 L 14106.00 -42605.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 13154.00 -34829.00 M 14925.00 -33364.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 14736.00 -33850.00 M 14993.00 -33308.00 L 14413.00 -33459.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 12784.00 -18057.00 M 14555.00 -16594.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 14365.00 -17079.00 M 14623.00 -16538.00 L 14042.00 -16688.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 10203.00 -6420.00 M 11270.00 -6420.00 L S 75 w 0 c 0 j 2 i [100 400] 0 d 0.00 G k R R S N 10754.00 -5815.00 M 10754.00 -7112.00 L S 75 w 0 c 0 j 2 i [100 400] 0 d 0.00 G k R R S 7797 -4435 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 7806 -5153 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 7651 -8208 M /Times-Roman-ISOLatin1 F 800 o f (62) h R S 7652 -8936 M /Times-Roman-ISOLatin1 F 800 o f (63) h R S 8299 -3638 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 9159 -3368 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 9109 -9691 M /Times-Roman-ISOLatin1 F 800 o f (7) h R S 9960 -9762 M /Times-Roman-ISOLatin1 F 800 o f (6) h R S 13016 -9692 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 13835 -9692 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 8804 -10813 M /Times-Roman-ISOLatin1 F 800 o f (MSB) h R S 12578 -10813 M /Times-Roman-ISOLatin1 F 800 o f (LSB) h R S 5934 -18462 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 27733 -25901 M /Times-Roman-ISOLatin1 F 800 o f (7) h R S 28232 -25901 M /Times-Roman-ISOLatin1 F 800 o f (6) h R S 28729 -25900 M /Times-Roman-ISOLatin1 F 800 o f (5) h R S 29338 -25901 M /Times-Roman-ISOLatin1 F 800 o f (4) h R S 28157 -34924 M /Times-Roman-ISOLatin1 F 800 o f (3) h R S 5754 -35249 M /Times-Roman-ISOLatin1 F 800 o f (3) h R S 5754 -35719 M /Times-Roman-ISOLatin1 F 800 o f (4) h R S 5754 -36191 M /Times-Roman-ISOLatin1 F 800 o f (5) h R S 5559 -44264 M /Times-Roman-ISOLatin1 F 800 o f (61) h R S 5559 -44889 M /Times-Roman-ISOLatin1 F 800 o f (62) h R S 5560 -45516 M /Times-Roman-ISOLatin1 F 800 o f (63) h R S 28498 -46101 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S N 9232.00 -2405.00 M 12267.00 -1312.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 11925.00 -1704.00 M 12351.00 -1281.00 L 11753.00 -1227.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 7044.00 -17494.00 M 10906.00 -17494.00 L 10906.00 -18296.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 7499.00 -17223.00 M 11289.00 -17223.00 L 11289.00 -18060.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 3940 -51149 M /Times-Roman-ISOLatin1 F 1000 o f (Figure 11. Spectral Selection and Successive Approximation Methods of Progressive Encoding) h R S N 29672.00 -24989.00 M 29672.00 -21743.00 L 36017.00 -17076.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 18315.00 -5036.00 M 20075.00 -4182.00 L S 75 w 0 c 0 j 2 i [100 400] 0 d 0.00 G k R R S N 19098.00 -4110.00 M 19098.00 -5323.00 L S 75 w 0 c 0 j 2 i [100 400] 0 d 0.00 G k R R S N 14358.00 -3042.00 M 16000.00 -2471.00 L S 75 w 0 c 0 j 2 i [100 400] 0 d 0.00 G k R R S N 14684.00 -2542.00 M 15662.00 -2970.00 L S 75 w 0 c 0 j 2 i [100 400] 0 d 0.00 G k R R S N 10224.00 -6462.00 M 11658.00 -6462.00 L S 75 w 0 c 0 j 2 i [100 400] 0 d 0.00 G k R R S N 10875.00 -5678.00 M 10875.00 -7319.00 L S 75 w 0 c 0 j 2 i [100 400] 0 d 0.00 G k R R S N 6893.00 -4894.00 M 6893.00 -7995.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 6640.00 -7540.00 M 6893.00 -8084.00 L 7147.00 -7540.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 14019 -17828 M /Times-Roman-ISOLatin1 F 800 o f (sending) h R S 7146 -46597 M /Times-Roman-ISOLatin1 F 800 o f (n) h 0.0 358.0 m (th) h 0 -358.0 m ( scan) h R S 3868 -49347 M /Times-Roman-ISOLatin1 F 900 o f (c\) progressive encoding: spectral selection) h R S 22272 -49418 M /Times-Roman-ISOLatin1 F 900 o f (d\) progressive encoding: successive approximation) h R S 6761 -39209 M /Symbol F 800 o f (\267) h R S 6761 -40349 M /Symbol F 800 o f (\267) h R S 6761 -41490 M /Symbol F 800 o f (\267) h R S 28181 -38240 M /Symbol F 800 o f (\267) h R S 28181 -39379 M /Symbol F 800 o f (\267) h R S 28181 -40518 M /Symbol F 800 o f (\267) h R S 8608 -8890 5712 5048 @ S 0.00 G - + * E R S 100 w 0 c 0 j 2 i 0.00 G k R R S N 8480.00 -3864.00 M 19987.00 -616.00 L 24607.00 -616.00 L 14376.00 -3864.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 14339.00 -8897.00 M 24606.00 -4823.00 L 24606.00 -751.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 9448.00 -3798.00 M 20752.00 -618.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 10340.00 -3798.00 M 21712.00 -553.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 13375.00 -3864.00 M 23711.00 -552.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 12411.00 -3864.00 M 22746.00 -552.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 9310.00 -3667.00 M 14822.00 -3667.00 L 14822.00 -8565.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 9792.00 -3468.00 M 15305.00 -3468.00 L 15305.00 -8366.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 8690.00 -4528.00 M 14384.00 -4528.00 L 24606.00 -1214.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 8690.00 -5190.00 M 14359.00 -5190.00 L 24537.00 -1878.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 8690.00 -8234.00 M 14359.00 -8234.00 L 24606.00 -4194.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 8690.00 -7504.00 M 14336.00 -7504.00 L 24537.00 -3533.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 9517.00 -3864.00 M 9517.00 -8964.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 10413.00 -3864.00 M 10413.00 -8964.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 13581.00 -3864.00 M 13581.00 -8964.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 12686.00 -3864.00 M 12686.00 -8964.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 26725.00 -22712.00 M 26725.00 -23700.00 L S 150 w 0 c 0 j [100 400] 0 d 0.00 G k R R S 26651 -22398 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 26377 -24313 M /Times-Roman-ISOLatin1 F 800 o f (62) h R S 26377 -25040 M /Times-Roman-ISOLatin1 F 800 o f (63) h R S 26619 -21752 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 26256 -17201 4043 750 @ S 0.00 G - + * E R S 75 w 0 c 0 j 2 i 0.00 G k R R S N 26307.00 -16481.00 M 32866.00 -11908.00 L 36293.00 -11908.00 L 30353.00 -16453.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 30384.00 -17169.00 M 36306.00 -12642.00 L 36306.00 -11896.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 26324 -18004 M /Times-Roman-ISOLatin1 F 800 o f (7 . . . . 0) h R S 25568 -17191 M /Times-Roman-ISOLatin1 F 800 o f (0) h R S 26706 -19382 M /Times-Roman-ISOLatin1 F 800 o f (1) h 0.0 358.0 m (st) h 0 -358.0 m ( scan) h R S 22215 -6305 4985 7815 @ S 0.00 G - + * E R R S 17516 -1346 7671 1999 @ S 0.00 G - + * E R R S N 17439.00 -1330.00 M 22168.00 -1330.00 L 22168.00 -5748.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 28685 -9812 4043 3950 @ S 0.00 G - + * E R S 100 w 0 c 0 j 2 i 0.00 G k R R S N 28684.00 -5898.00 M 35241.00 -149.00 L 38669.00 -149.00 L 32728.00 -5866.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 38633.00 -149.00 M 38633.00 -3395.00 L 32803.00 -9738.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 29391.00 -5360.00 M 33271.00 -5360.00 L 33271.00 -9272.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 29771.00 -4897.00 M 33706.00 -4897.00 L 33706.00 -8811.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 35650.00 -4967.00 M 36962.00 -3846.00 L S 150 w 0 c 0 j [100 400] 0 d 0.00 G k R R S 27998 -11153 M /Times-Roman-ISOLatin1 F 1000 o f (\(b\) Sequential encoding) h R S 36964 -6785 M /Times-Roman-ISOLatin1 F 800 o f (sending) h R S N 35852.00 -7340.00 M 37402.00 -5494.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 37304.00 -6005.00 M 37459.00 -5426.00 L 36916.00 -5679.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 33515.00 -3361.00 M 34771.00 -2174.00 L S 150 w 0 c 0 j [100 400] 0 d 0.00 G k R R S 6408 -27700 4044 1319 @ S 0.00 G - + * E R S 100 w 0 c 0 j 2 i 0.00 G k R R S N 6459.00 -26412.00 M 13019.00 -21838.00 L 16445.00 -21838.00 L 10505.00 -26384.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 6901.00 -26103.00 M 10756.00 -26103.00 L 10756.00 -27444.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 7363.00 -25797.00 M 11218.00 -25797.00 L 11218.00 -27189.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 16436.00 -21894.00 M 16436.00 -23094.00 L 10508.00 -27680.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 6487.00 -27121.00 M 10508.00 -27121.00 L 16488.00 -22585.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 6533 -29311 M /Times-Roman-ISOLatin1 F 800 o f (2) h 0.0 358.0 m (nd) h 0 -358.0 m ( scan) h R S 14094 -26658 M /Times-Roman-ISOLatin1 F 800 o f (sending) h R S N 13154.00 -26562.00 M 14925.00 -25096.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 14736.00 -25582.00 M 14993.00 -25040.00 L 14413.00 -25191.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S 5825 -26910 M /Times-Roman-ISOLatin1 F 800 o f (1) h R S 5826 -27665 M /Times-Roman-ISOLatin1 F 800 o f (2) h R S 6407 -18554 4044 752 @ S 0.00 G - + * E R S 75 w 0 c 0 j 2 i 0.00 G k R R S N 6458.00 -17835.00 M 13018.00 -13262.00 L 16444.00 -13262.00 L 10505.00 -17805.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R S N 10535.00 -18523.00 M 16459.00 -13996.00 L 16459.00 -13249.00 L S 75 w 0 c 0 j 2 i 0.00 G k R R R R R S 29816 -75834 M /Times-Roman-ISOLatin1 F 1000 o f (14) h R showpage $P e %%Page: 15 15 /$P a D g N 0 79200 T S S 7200 -2700 T N 0 G 300 -1200 M -7200 2700 T R S 7200 -74700 T N 0 G 300 -1200 M -7200 74700 T R R S 7192 -7189 T N 0 G 300 -1200 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1200 o f (10 Other Aspects of the JPEG Proposal) h 300 -2950 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 59.4 0 32 (Some key aspects of the proposed standard can only) W 300 -4050 M 250.3 0 32 (be mentioned briefly. Foremost among these are) W 300 -5150 M 556.2 0 32 (points concerning the coded representation for) W 300 -6250 M 159.0 0 32 (compressed image data specified in addition to the) W 300 -7350 M (encoding and decoding procedures.) h 300 -8450 M 300 -9550 M 203.5 0 32 (Most importantly, an ) W /Times-Italic-ISOLatin1 $ /Times-Italic & P /Times-Italic-ISOLatin1 F 1000 o f 203.5 0 32 (interchange format) W /Times-Roman-ISOLatin1 F 1000 o f 203.5 0 32 ( syntax is) W 300 -10650 M 356.2 0 32 (specified which ensures that a JPEG\255compressed) W 300 -11750 M 567.6 0 32 (image can be exchanged successfully between) W 300 -12850 M 231.8 0 32 (different application environments. The format is) W 300 -13950 M 357.9 0 32 (structured in a consistent way for all modes of) W 300 -15050 M 139.5 0 32 (operation. The interchange format always includes) W 300 -16150 M 367.0 0 32 (all quantization and entropy\255coding tables which) W 300 -17250 M (were used to compress the image.) h 300 -18350 M 300 -19450 M 63.5 0 32 (Applications \(and application\255specific standards\) are) W 300 -20550 M 423.9 0 32 (the ) W 423.9 0 32 (\026) W 423.9 0 32 (users) W 423.9 0 32 (\027) W 423.9 0 32 ( of the JPEG standard. The JPEG) W 300 -21650 M 352.0 0 32 (standard imposes no requirement that, within an) W 300 -22750 M 315.2 0 32 (application's environment, all or even any tables) W 300 -23850 M 222.6 0 32 (must be encoded with the compressed image data) W 300 -24950 M 657.5 0 32 (during storage or transmission. This leaves) W 300 -26050 M 532.8 0 32 (applications the freedom to specify default or) W 300 -27150 M 103.0 0 32 (referenced tables if they are considered appropriate. ) W 300 -28250 M 135.5 0 32 (It also leaves them the responsibility to ensure that) W 300 -29350 M 993.3 0 32 (JPEG\255compliant decoders used within their) W 300 -30450 M 66.3 0 32 (environment get loaded with the proper tables at the) W 300 -31550 M 69.9 0 32 (proper times, and that the proper tables are included) W 300 -32650 M 72.0 0 32 (in the interchange format when a compressed image) W 300 -33750 M (is ) h (\026) h (exported) h (\027) h ( outside the application.) h 300 -34850 M 300 -35950 M 127.3 0 32 (Some of the important applications that are already) W 300 -37050 M 301.7 0 32 (in the process of adopting JPEG compression or) W 300 -38150 M 226.0 0 32 (have stated their interest in doing so are Adobe's) W 300 -39250 M 333.3 0 32 (PostScript language for printing systems [1], the) W 300 -40350 M 87.6 0 32 (Raster Content portion of the ISO Office Document) W 300 -41450 M 47.2 0 32 (Architecture and Interchange Format [13], the future) W 300 -42550 M 185.7 0 32 (CCITT color facsimile standard, and the European) W 300 -43650 M (ETSI videotext standard [10].) h 300 -44750 M 300 -45850 M 300 -47100 M /Times-Bold-ISOLatin1 F 1200 o f (11 Standardization Schedule) h 300 -48850 M /Times-Roman-ISOLatin1 F 1000 o f 76.4 0 32 (JPEG's ISO standard will be divided into two parts. ) W 300 -49950 M 114.4 0 32 (Part 1 [2] will specify the four modes of operation,) W 300 -51050 M 147.4 0 32 (the different codecs specified for those modes, and) W 300 -52150 M 423.9 0 32 (the interchange format. It will also contain a) W 300 -53250 M 131.8 0 32 (substantial informational section on implementation) W 300 -54350 M 180.8 0 32 (guidelines. Part 2 [3] will specify the compliance) W 300 -55450 M 458.8 0 32 (tests which will determine whether an encoder) W 300 -56550 M 433.6 0 32 (implementation, a decoder implementation, or a) W 300 -57650 M 618.8 0 32 (JPEG\255compressed image in interchange format) W 300 -58750 M 40.1 0 32 (comply with the Part 1 specifications. In addition to) W 300 -59850 M 222.8 0 32 (the ISO documents referenced, the JPEG standard) W 300 -60950 M (will also be issued as CCITT Recommendation T.81.) h 300 -62050 M -7192 7189 T R S 32040 -7189 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 F 1000 o f 378.8 0 32 (There are two key balloting phases in the ISO) W 300 -2150 M 125.3 0 32 (standardization process: a Committee Draft \(CD\) is) W 300 -3250 M 1011.2 0 32 (balloted to determine promotion to Draft) W 300 -4350 M 0.3 0 32 (International Standard \(DIS\), and a DIS is balloted to) W 300 -5450 M 139.2 0 32 (determine promotion to International Standard \(IS\). ) W 300 -6550 M 545.1 0 32 (A CD ballot requires four to six months of) W 300 -7650 M 271.0 0 32 (processing, and a DIS ballot requires six to nine) W 300 -8750 M 243.1 0 32 (months of processing. JPEG's Part 1 began DIS) W 300 -9850 M 312.6 0 32 (ballot in November 1991, and Part 2 began CD) W 300 -10950 M (ballot in December 1991.) h 300 -12050 M 300 -13150 M 111.3 0 32 (Though there is no guarantee that the first ballot of) W 300 -14250 M 3.1 0 32 (each phase will result in promotion to the next, JPEG) W 300 -15350 M 5.1 0 32 (achieved promotion of CD Part 1 to DIS Part 1 in the) W 300 -16450 M 371.6 0 32 (first ballot. Moreover, JPEG's DIS Part 1 has) W 300 -17550 M 264.5 0 32 (undergone no technical changes \(other than some) W 300 -18650 M 23.7 0 32 (minor corrections\) since JPEG's final Working Draft) W 300 -19750 M 170.6 0 32 (\(WD\) [14]. Thus, Part 1 has remained unchanged) W 300 -20850 M 38.0 0 32 (from the final WD, through CD, and into DIS. If all) W 300 -21950 M 59.0 0 32 (goes well, Part 1 should receive final approval as an) W 300 -23050 M 46.2 0 32 (IS in mid\2551992, with Part 2 getting final IS approval) W 300 -24150 M (about nine months later. ) h 300 -25250 M 300 -26350 M 300 -27600 M /Times-Bold-ISOLatin1 F 1200 o f (12 Conclusions) h 300 -29350 M /Times-Roman-ISOLatin1 F 1000 o f 965.5 0 32 (The emerging JPEG continuous\255tone image) W 300 -30450 M 17.6 0 32 (compression standard is not a panacea that will solve) W 300 -31550 M 190.9 0 32 (the myriad issues which must be addressed before) W 300 -32650 M 100.6 0 32 (digital images will be fully integrated within all the) W 300 -33750 M 157.3 0 32 (applications that will ultimately benefit from them. ) W 300 -34850 M 241.2 0 32 (For example, if two applications cannot exchange) W 300 -35950 M 22.8 0 32 (uncompressed images because they use incompatible) W 300 -37050 M 190.9 0 32 (color spaces, aspect ratios, dimensions, etc. then a) W 300 -38150 M (common compression method will not help.) h 300 -39250 M 300 -40350 M 100.0 0 32 (However, a great many applications are ) W 100.0 0 32 (\026) W 100.0 0 32 (stuck) W 100.0 0 32 (\027) W 100.0 0 32 ( be\255) W 300 -41450 M 21.4 0 32 (cause of storage or transmission costs, because of ar\255) W 300 -42550 M 632.5 0 32 (gument over which \(nonstandard\) compression) W 300 -43650 M 114.7 0 32 (method to use, or because VLSI codecs are too ex\255) W 300 -44750 M 52.1 0 32 (pensive due to low volumes. For these applications,) W 300 -45850 M 105.8 0 32 (the thorough technical evaluation, testing, selection,) W 300 -46950 M 339.0 0 32 (validation, and documentation work which JPEG) W 300 -48050 M 153.3 0 32 (committee members have performed is expected to) W 300 -49150 M 227.2 0 32 (soon yield an approved international standard that) W 300 -50250 M 111.0 0 32 (will withstand the tests of quality and time. As di\255) W 300 -51350 M 100.4 0 32 (verse imaging applications become increasingly im\255) W 300 -52450 M 216.8 0 32 (plemented on open networked computing systems,) W 300 -53550 M 32.0 0 32 (the ultimate measure of the committee's success will) W 300 -54650 M 180.8 0 32 (be when JPEG\255compressed digital images come to) W 300 -55750 M 111.8 0 32 (be regarded and even taken for granted as ) W 111.8 0 32 (\026) W 111.8 0 32 (just an\255) W 300 -56850 M (other data type,) h (\027) h ( as text and graphics are today.) h 300 -58250 M 300 -59350 M 300 -60450 M 300 -61550 M 300 -62650 M 300 -63750 M -32040 7189 T R S 29912 -75834 M /Times-Roman-ISOLatin1 F 1000 o f (15) h R showpage $P e %%Page: 16 16 /$P a D g N 0 79200 T S S 7200 -2700 T N 0 G 300 -1200 M -7200 2700 T R S 7200 -74700 T N 0 G 300 -1200 M -7200 74700 T R R S 7200 -7200 T N 0 G 300 -1200 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1200 o f (For more information) h 300 -2950 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f 114.8 0 32 (Information on how to obtain the ISO JPEG \(draft\)) W 300 -4050 M 177.4 0 32 (standards can be obtained by writing the author at) W 300 -5150 M (the following address:) h 300 -6250 M 300 -7350 M (Digital Equipment Corporation) h 300 -8450 M (146 Main Street, ML01\2552/U44) h 300 -9550 M (Maynard, MA 01754\2552571) h 300 -10650 M 300 -11750 M (Internet: wallace@gauss.enet.dec.com) h 300 -12850 M 300 -13950 M 76.5 0 32 (Floppy disks containing uncompressed, compressed,) W 300 -15050 M 72.0 0 32 (and reconstructed data for the purpose of informally) W 300 -16150 M 956.4 0 32 (validating whether an encoder or decoder) W 300 -17250 M 200.2 0 32 (implementation conforms to the proposed standard) W 300 -18350 M 488.3 0 32 (are available. Thanks to the following JPEG) W 300 -19450 M 412.3 0 32 (committee member and his company who have) W 300 -20550 M 105.4 0 32 (agreed to provide these for a nominal fee on behalf) W 300 -21650 M 24.8 0 32 (of the committee until arrangements can be made for) W 300 -22750 M (ISO to provide them:) h 300 -23850 M 300 -24950 M (Eric Hamilton) h 300 -26050 M (C\255Cube Microsystems) h 300 -27150 M (1778 McCarthy Blvd.) h 300 -28250 M (Milpitas, CA 95035) h 300 -29350 M 300 -30450 M 300 -31700 M /Times-Bold-ISOLatin1 F 1200 o f (Acknowledgments) h 300 -33450 M /Times-Roman-ISOLatin1 F 1000 o f 217.8 0 32 (The following longtime JPEG core members have) W 300 -34550 M 52.1 0 32 (spent untold hours \(usually in addition to their ``real) W 300 -35650 M 51.3 0 32 (jobs''\) to make this collaborative international effort) W 300 -36750 M 60.1 0 32 (succeed. Each has made specific substantive contri\255) W 300 -37850 M 111.1 0 32 (butions to the JPEG proposal: Aharon Gill \(Zoran,) W 300 -38950 M 130.2 0 32 (Israel\), Eric Hamilton \(C\255Cube, USA\), Alain Leger) W 300 -40050 M 667.3 0 32 (\(CCETT, France\), Adriaan Ligtenberg \(Storm,) W 300 -41150 M 195.4 0 32 (USA\), Herbert Lohscheller \(ANT, Germany\), Joan) W 300 -42250 M 88.3 0 32 (Mitchell \(IBM, USA\), Michael Nier \(Kodak, USA\),) W 300 -43350 M 211.8 0 32 (Takao Omachi \(NEC, Japan\), William Pennebaker) W 300 -44450 M 189.2 0 32 (\(IBM, USA\), Henning Poulsen \(KTAS, Denmark\),) W 300 -45550 M 292.5 0 32 (and Jorgen Vaaben \(AutoGraph, Denmark\). The) W 300 -46650 M 153.5 0 32 (leadership efforts of Hiroshi Yasuda \(NTT, Japan\),) W 300 -47750 M 97.2 0 32 (the Convenor of JTC1/SC2/WG8 from which JPEG) W 300 -48850 M 6.2 0 32 (was spawned, Istvan Sebestyen \(Siemens, Germany\),) W 300 -49950 M 278.2 0 32 (the Special Rapporteur from CCITT SGVIII, and) W 300 -51050 M 445.0 0 32 (Graham Hudson \(British Telecom U.K.\) former) W 300 -52150 M 94.4 0 32 (JPEG chair and founder of the effort which became) W 300 -53250 M 34.2 0 32 (JPEG. The author regrets that space does not permit) W 300 -54350 M 111.3 0 32 (recognition of the many other individuals who con\255) W 300 -55450 M (tributed to JPEG's work.) h 300 -57150 M 17.6 0 32 (Thanks to Majid Rabbani of Eastman Kodak for pro\255) W 300 -58250 M (viding the example in section 7.3.) h 300 -59950 M 24.5 0 32 (The author's role within JPEG has been supported in) W 300 -61050 M 121.8 0 32 (a great number of ways by Digital Equipment Cor\255) W 300 -62150 M (poration ) h 300 -64000 M -7200 7200 T R S 32040 -7200 T N 0 G 300 -1200 M /Times-Bold-ISOLatin1 F 1200 o f (References) h 300 -2950 M /Times-Roman-ISOLatin1 F 1000 o f (1.) h 2100 -2950 M 23.4 0 32 (Adobe Systems Inc. ) W /Times-Italic-ISOLatin1 $ /Times-Italic & P /Times-Italic-ISOLatin1 F 1000 o f 23.4 0 32 (PostScript Language Refer\255) W 2100 -4050 M 320.7 0 32 (ence Manual) W /Times-Roman-ISOLatin1 F 1000 o f 320.7 0 32 (. Second Ed. Addison Wesley,) W 2100 -5150 M (Menlo Park, Calif. 1990) h 300 -6850 M (2.) h 2100 -6850 M 17.4 0 32 (Digital Compression and Coding of Continuous\255) W 2100 -7950 M 362.0 0 32 (tone Still Images, Part 1, Requirements and) W 2100 -9050 M 168.0 0 32 (Guidelines. ISO/IEC JTC1 Draft International) W 2100 -10150 M (Standard 10918\2551, Nov. 1991.) h 300 -11850 M (3.) h 2100 -11850 M 17.4 0 32 (Digital Compression and Coding of Continuous\255) W 2100 -12950 M 181.3 0 32 (tone Still Images, Part 2, Compliance Testing. ) W 2100 -14050 M 129.0 0 32 (ISO/IEC JTC1 Committee Draft 10918\2552, Dec.) W 2100 -15150 M (1991.) h 300 -16850 M (4.) h 2100 -16850 M 329.2 0 32 (Encoding parameters of digital television for) W 2100 -17950 M 140.0 0 32 (studios. CCIR Recommendations, Recommen\255) W 2100 -19050 M (dation 601, 1982.) h 300 -20750 M (5.) h 2100 -20750 M 18.3 0 32 (Howard, P.G., and Vitter, J.S. New methods for) W 2100 -21850 M 445.8 0 32 (lossless image compression using arithmetic) W 2100 -22950 M 186.2 0 32 (coding. Brown University Dept. of Computer) W 2100 -24050 M (Science Tech. Report No. CS\25591\25547, Aug. 1991.) h 300 -25750 M (6.) h 2100 -25750 M 68.0 0 32 (Hudson, G.P. The development of photographic) W 2100 -26850 M 53.0 0 32 (videotex in the UK. In ) W /Times-Italic-ISOLatin1 F 1000 o f 53.0 0 32 (Proceedings of the IEEE) W 2100 -27950 M 243.0 0 32 (Global Telecommunications Conference, IEEE) W 2100 -29050 M (Communication Society,) h /Times-Roman-ISOLatin1 F 1000 o f ( 1983, pp. 319\255322.) h 300 -30750 M (7.) h 2100 -30750 M 261.3 0 32 (Hudson, G.P., Yasuda, H., and Sebesty\351n,) W 300.0 0.0 m 261.3 0 32 ( ) W 261.3 0 32 (I. ) W 2100 -31850 M 167.8 0 32 (The international standardization of a still pic\255) W 2100 -32950 M 117.0 0 32 (ture compression technique. In ) W /Times-Italic-ISOLatin1 F 1000 o f 117.0 0 32 (Proceedings of) W 2100 -34050 M 251.5 0 32 (the IEEE Global Telecommunications Confer\255) W 2100 -35150 M 606.0 0 32 (ence, IEEE Communications Society,) W /Times-Roman-ISOLatin1 F 1000 o f 606.0 0 32 ( Nov.) W 2100 -36250 M (1988, pp. 1016\2551021.) h 300 -37950 M (8.) h 2100 -37950 M 136.0 0 32 (Huffman, D.A. A method for the construction) W 2100 -39050 M 52.2 0 32 (of minimum redundancy codes. In ) W /Times-Italic-ISOLatin1 F 1000 o f 52.2 0 32 (Proceedings) W 2100 -40150 M (IRE) h /Times-Roman-ISOLatin1 F 1000 o f (, vol. 40, 1962, pp. 1098\2551101.) h 300 -41850 M (9.) h 2100 -41850 M 186.7 0 32 (L\351ger, A. Implementations of fast discrete co\255) W 2100 -42950 M 214.3 0 32 (sine transform for full color videotex services) W 2100 -44050 M 342.3 0 32 (and terminals. In ) W /Times-Italic-ISOLatin1 F 1000 o f 342.3 0 32 (Proceedings of the IEEE) W 2100 -45150 M 243.0 0 32 (Global Telecommunications Conference, IEEE) W 2100 -46250 M (Communications Society,) h /Times-Roman-ISOLatin1 F 1000 o f ( 1984, pp. 333\255337.) h 300 -47950 M (10.) h 2100 -47950 M 216.5 0 32 (L\351ger, A., Omachi, T., and Wallace, G. The) W 2100 -49050 M 246.2 0 32 (JPEG still picture compression algorithm. In) W 2100 -50150 M /Times-Italic-ISOLatin1 F 1000 o f 72.1 0 32 (Optical Engineering) W /Times-Roman-ISOLatin1 F 1000 o f 72.1 0 32 (, vol. 30, no. 7 \(July 1991\),) W 2100 -51250 M (pp. 947\255954.) h 300 -52950 M (11.) h 2100 -52950 M 42.5 0 32 (L\351ger, A., Mitchell, M., and Yamazaki, Y. Still) W 2100 -54050 M 18.2 0 32 (picture compression algorithms evaluated for in\255) W 2100 -55150 M 223.6 0 32 (ternational standardization. In P) W /Times-Italic-ISOLatin1 F 1000 o f 223.6 0 32 (roceedings of) W 2100 -56250 M 251.5 0 32 (the IEEE Global Telecommunications Confer\255) W 2100 -57350 M 606.0 0 32 (ence, IEEE Communications Society,) W /Times-Roman-ISOLatin1 F 1000 o f 606.0 0 32 ( Nov.) W 2100 -58450 M (1988, pp. 1028\2551032.) h 300 -60150 M (12.) h 2100 -60150 M 168.0 0 32 (Lohscheller, H. A subjectively adapted image) W 2100 -61250 M 89.8 0 32 (communication system. ) W /Times-Italic-ISOLatin1 F 1000 o f 89.8 0 32 (IEEE Trans. Commun.) W /Times-Roman-ISOLatin1 F 1000 o f 89.8 0 32 ( ) W 2100 -62350 M (COM\25532 \(Dec. 1984\), pp. 1316\2551322.) h 2100 -63450 M -32040 7200 T R S 29720 -76121 M /Times-Roman-ISOLatin1 F 1000 o f (16) h R showpage $P e %%Page: 17 17 /$P a D g N 0 79200 T S S 7200 -2700 T N 0 G 300 -1200 M -7200 2700 T R S 7200 -74700 T N 0 G 300 -1200 M -7200 74700 T R R S 7200 -7200 T N 0 G 300 -1050 M /Times-Roman-ISOLatin1 $ /Times-Roman & P /Times-Roman-ISOLatin1 F 1000 o f (13.) h 2100 -1050 M 19.0 0 32 (Office Document Architecture \(ODA\) and Inter\255) W 2100 -2150 M 16.9 0 32 (change Format, Part 7: Raster Graphics Content) W 2100 -3250 M 536.5 0 32 (Architectures. ISO/IEC JTC1 International) W 2100 -4350 M (Standard 8613\2557.) h 300 -6050 M (14.) h 2100 -6050 M 307.5 0 32 (Pennebaker, W.B., JPEG Tech. Specification,) W 2100 -7150 M 257.0 0 32 (Revision 8. Informal Working paper JPEG\2558\255) W 2100 -8250 M (R8, Aug. 1990.) h 300 -9950 M (15.) h 2100 -9950 M 108.1 0 32 (Pennebaker, W.B., Mitchell, J.L., et. al. Arith\255) W 2100 -11050 M 53.1 0 32 (metic coding articles. ) W /Times-Italic-ISOLatin1 $ /Times-Italic & P /Times-Italic-ISOLatin1 F 1000 o f 53.1 0 32 (IBM J. Res. Dev., ) W /Times-Roman-ISOLatin1 F 1000 o f 53.1 0 32 (vol. 32,) W 2100 -12150 M (no. 6 \(Nov. 1988\), pp. 717\255774.) h 300 -13850 M (16.) h 2100 -13850 M 649.0 0 32 (Rao, K.R., and Yip, P. ) W /Times-Italic-ISOLatin1 F 1000 o f 649.0 0 32 (Discrete Cosine) W 2100 -14950 M 558.0 0 32 (Transform\255\255Algorithms, Advantages, Applica\255) W 2100 -16050 M (tions) h /Times-Roman-ISOLatin1 F 1000 o f (. Academic Press, Inc. London, 1990.) h 300 -17750 M (17.) h 2100 -17750 M 129.4 0 32 (Standardization of Group 3 facsimile apparatus) W 2100 -18850 M 23.4 0 32 (for document transmission. CCITT Recommen\255) W 2100 -19950 M 272.5 0 32 (dations, Fascicle VII.2, Recommendation T.4,) W 2100 -21050 M (1980.) h 300 -22750 M (18.) h 2100 -22750 M 912.8 0 32 (Wallace, G.K. Overview of the JPEG) W 2100 -23850 M 119.5 0 32 (\(ISO/CCITT\) still image compression standard. ) W 2100 -24950 M 217.0 0 32 (Image Processing Algorithms and Techniques. ) W 2100 -26050 M 294.6 0 32 (In ) W /Times-Italic-ISOLatin1 F 1000 o f 294.6 0 32 (Proceedings of the SPIE) W /Times-Roman-ISOLatin1 F 1000 o f 294.6 0 32 (, vol. 1244 \(Feb.) W 2100 -27150 M (1990\), pp. 220\255233.) h 300 -28850 M (19.) h 2100 -28850 M 118.9 0 32 (Wallace, G., Vivian, R,. and Poulsen, H. Sub\255) W 2100 -29950 M 158.5 0 32 (jective testing results for still picture compres\255) W 2100 -31050 M 8.5 0 32 (sion algorithms for international standardization. ) W 2100 -32150 M 56.8 0 32 (In ) W /Times-Italic-ISOLatin1 F 1000 o f 56.8 0 32 (Proceedings of the IEEE Global Telecommu\255) W 2100 -33250 M 272.3 0 32 (nications Conference. IEEE Communications) W 2100 -34350 M (Society,) h /Times-Roman-ISOLatin1 F 1000 o f ( Nov. 1988, pp. 1022\2551027.) h 300 -36050 M ( ) h 300 -37900 M /Times-Bold-ISOLatin1 $ /Times-Bold & P /Times-Bold-ISOLatin1 F 1200 o f (Biography) h 300 -39050 M 300 -40150 M /Times-Roman-ISOLatin1 F 1000 o f 602.7 0 32 (Gregory K. Wallace is currently Manager of) W 300 -41250 M 35.3 0 32 (Multimedia Engineering, Advanced Development, at) W 300 -42350 M 185.2 0 32 (Digital Equipment Corporation. Since 1988 he has) W 300 -43450 M 222.4 0 32 (served as Chair of the JPEG committee \(ISO/IEC) W 300 -44550 M 100.8 0 32 (JTC1/SC2/WG10\). For the past five years at DEC,) W 300 -45650 M 199.3 0 32 (he has worked on efficient software and hardware) W 300 -46750 M 979.3 0 32 (implementations of image compression and) W 300 -47850 M 1118.3 0 32 (processing algorithms for incorporation in) W 300 -48950 M 39.6 0 32 (general\255purpose computing systems. He received the) W 300 -50050 M 95.1 0 32 (BSEE and MSEE from Stanford University in 1977) W 300 -51150 M 369.7 0 32 (and 1979. His current research interests are the) W 300 -52250 M 1132.0 0 32 (integration of robust real\255time multimedia) W 300 -53350 M (capabilities into networked computing systems. ) h 300 -54450 M 300 -56150 M 300 -57546 M -7200 7200 T R S 32040 -7200 T N 0 G -32040 7200 T R S 29912 -76888 M /Times-Roman-ISOLatin1 F 1000 o f (17) h R showpage $P e $D restore %%Trailer end % DEC_WRITE_dict %%Pages: 17 %%DocumentFonts: Times-Italic-ISOLatin1 %%+ Times-Roman-ISOLatin1 %%+ Times-Bold-ISOLatin1 %%+ Helvetica-Bold-ISOLatin1 %%+ Helvetica-ISOLatin1 %%+ Symbol %%+ Courier-ISOLatin1 %%+ Dutch801-Italic-DECmath_Italic %%+ Dutch801-Roman-DECmath_Extension %%+ Dutch801-Roman-DECmath_Symbol