www.pudn.com > SolutionsforMultiuserDetection.rar > 2.11.rickard.ps

%!PS (but not EPSF; comments have been disabled)
%DVIPSCommandLine: dvips prob0211 -o 2.11.rickard.ps
%DVIPSParameters: dpi=600, compressed, comments removed
%DVIPSSource:  TeX output 1999.02.18:0851
/TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N
/X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72
mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1}
ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale
isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div
hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul
TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if}
forall round exch round exch]setmatrix}N /@landscape{/isls true N}B
/@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B
/FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{
/nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N
string /base X array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N
end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{
/sf 1 N /fntrx FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0]
N df-tail}B /E{pop nn dup definefont setfont}B /ch-width{ch-data dup
length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{
128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub
get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data
dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N
/rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup
/base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx
0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff
setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff
.1 sub]/id ch-image N /rw ch-width 7 add 8 idiv string N /rc 0 N /gp 0 N
/cp 0 N{rc 0 ne{rc 1 sub /rc X rw}{G}ifelse}imagemask restore}B /G{{id
gp get /gp gp 1 add N dup 18 mod S 18 idiv pl S get exec}loop}B /adv{cp
add /cp X}B /chg{rw cp id gp 4 index getinterval putinterval dup gp add
/gp X adv}B /nd{/cp 0 N rw exit}B /lsh{rw cp 2 copy get dup 0 eq{pop 1}{
dup 255 eq{pop 254}{dup dup add 255 and S 1 and or}ifelse}ifelse put 1
adv}B /rsh{rw cp 2 copy get dup 0 eq{pop 128}{dup 255 eq{pop 127}{dup 2
idiv S 128 and or}ifelse}ifelse put 1 adv}B /clr{rw cp 2 index string
putinterval adv}B /set{rw cp fillstr 0 4 index getinterval putinterval
adv}B /fillstr 18 string 0 1 17{2 copy 255 put pop}for N /pl[{adv 1 chg}
{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{
adv rsh nd}{1 add adv}{/rc X nd}{1 add set}{1 add clr}{adv 2 chg}{adv 2
chg nd}{pop nd}]dup{bind pop}forall N /D{/cc X dup type /stringtype ne{]
}if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup
length 1 sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{
cc 1 add D}B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin
0 0 moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul
add .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore userdict
/eop-hook known{eop-hook}if showpage}N /@start{userdict /start-hook
known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X
/IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for
65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0
0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V
{}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7
getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false}
ifelse}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale rulex ruley false
RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR rulex ruley scale 1 1
false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave newpath transform
round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg
rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail
{dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail}B /c{-4 M}
B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{3 M}B /k{
4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w}B /q{
p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{3 2 roll p
a}B /bos{/SS save N}B /eos{SS restore}B end
TeXDict begin 40258431 52099146 1000 600 600 (prob0211.dvi)
@start /Fa 5 104 df<007FB81280B912C0A26C17803204799641>0
D<181EA4181F84A285180785727EA2727E727E85197E85F11F80F10FC0F107F0007FBA12
FCBCFCA26C19FCCCEA07F0F10FC0F11F80F13F00197E61614E5A4E5AA24E5A61180F96C7
FCA260181EA4482C7BAA53>33 D<91381FFFFE91B6FC1303010F14FED91FF0C7FCEB7F80
01FEC8FCEA01F8485A485A485A5B48C9FCA2123EA25AA2127812F8A25AA2B712FE16FFA2
16FE00F0C9FCA27EA21278127CA27EA27EA26C7E7F6C7E6C7E6C7EEA00FEEB7F80EB1FF0
6DB512FE010314FF1300021F13FE283279AD37>50 D
102 D<12FCEAFFC0EA07F0EA01FCEA007E7F80131F80130FB3A7801307806D7E6D7EEB00
7EEC1FF0EC07F8EC1FF0EC7E00495A495A495A5C130F5CB3A7131F5C133F91C7FC137E48
5AEA07F0EAFFC000FCC8FC1D537ABD2A>I E /Fb 2 90 df88 DI
E /Fc 4 62 df48 D<13381378EA01F8121F12FE12E01200B3AB487EB512F8
A215267BA521>I<13FF000313E0380E03F0381800F848137C48137E00787F12FC6CEB1F
80A4127CC7FC15005C143E147E147C5C495A495A5C495A010EC7FC5B5B903870018013E0
EA0180390300030012065A001FB5FC5A485BB5FCA219267DA521>I<007FB712C0B812E0
A2CBFCABB812E0A26C16C02B117D9633>61 D E /Fd 5 107 df<48B61280000715C048
1580481500263C0C06C7FC127012C0EB1C0EEA0018A21338A2EB701EA313F013E0120114
1F120313C0000780A2380F800FA26C486CC7FC221A7D9827>25 D77
D
99 D<130E131F5BA2133E131C90C7FCA7EA03E0487EEA0C78EA187C1230A212605B12C0
A2EA01F0A3485AA2485AA2EBC180EA0F81A2381F0300A213066C5A131CEA07F06C5A1128
7DA617>105 D<1407EC0F80141FA21500140E91C7FCA7EB03E0EB07F8EB0C3C1318EB30
3E136013C0A248485AA2C7FCA25CA4495AA4495AA4495AA4495AA21238D87C1FC7FC12FC
133E485AEA70F8EA7FE0EA1F80193380A61B>I E /Fe 20 117 df11
DI<013FB612E090B712F05A120717E0270F807006C7FC391E00600E48140C003813
E04813C048141CEAC0011200148001035BA213071400A25B1578011E137CA3133E133C13
7C157E13FC5B1201157F1203497FA3D801C0131C2C257EA32F>25
D<121C127FEAFF80A5EA7F00121C0909798817>58 D<121C127FEAFF80A213C0A3127F12
1C1200A412011380A2120313005A1206120E5A5A5A12600A19798817>I<902603FFF893
383FFF80496081D900079438FF80000206DC01BFC7FCA2020E4C5A1A7E020C1606190CDA
1C7E16FE4F5A02181630A20238166162023016C1F00181DA703F158395380303F0026015
06A202E0ED0C076202C01518183001016D6C140F06605B028015C0A20103923801801FDD
03005B140092380FC00649173F4D91C8FC01065DA2010E4B5B4D137E130C6F6C5A011C17
FEDCE1805B011802E3C7FCA2013802E6130104EC5C1330ED03F8017016034C5C01F05CD8
07FC4C7EB500E0D9C007B512F01680150151397CB851>77 D<92391FE00380DBFFFC1300
02036D5A91390FE01F8F91393F0007DF027EEB01FE02F81300495A4948147E177C494814
3C495AA2011F153891C8FCA3491530A28094C7FC80806D7E14FEECFFE06D13FE6DEBFFC0
6D14F06D806D80021F7F02037FEC003F03037F1500167F163F161FA3120C160FA2001C15
1F94C7FCA3003C153EA25E003E5D127E007F4A5A6D495A6DEB0FC0D8F9F0495AD8F0FE01
FEC8FC39E03FFFF8010F13E0D8C00190C9FC313D7CBA33>83 D<0003B812FEA25A903AF8
003FC00101C0913880007E4848163C90C7007F141C121E001C92C7FCA2485CA200305C00
7017180060130112E0485CA21403C716005DA21407A25DA2140FA25DA2141FA25DA2143F
A25DA2147FA292C9FCA25CA25CA21301A25CA21303A25CEB0FFC003FB6FC5AA237397EB8
31>I<133FEA1FFFA3C67E137EA313FE5BA312015BA312035BA31207EBE0FCEBE3FF9038
E707C0390FFE03E09038F801F001F013F8EBE000485A15FC5BA2123F90C7FCA214015A12
7EA2140312FE4814F8A2140715F05AEC0FE0A215C0EC1F80143F00781400007C137E5C38
3C01F86C485A380F07C06CB4C7FCEA01FC1E3B7CB924>98 DI<163FED1FFFA3ED007F16
7EA216FEA216FCA21501A216F8A21503A216F0A21507A2027E13E0903803FF8790380FC1
CF90381F00EF017EEB7FC049133F485A4848131F000715805B000F143F485A1600485A5D
127F90C7127EA215FE5A485CA21401A248ECF80CA21403161CEDF0181407007C1538007E
010F1330003E131F027B13706C01E113E03A0F83C0F9C03A03FF007F80D800FCEB1F0028
3B7DB92B>I<16F8ED03FEED0F8792381F0F80ED3E3F167F157CA215FC1700161C4A48C7
FCA414035DA414075DA20107B512F0A39026000FE0C7FC5DA4141F5DA4143F92C8FCA45C
147EA514FE5CA413015CA4495AA45C1307A25C121E123F387F8F80A200FF90C9FC131E12
FEEA7C3CEA7878EA1FF0EA07C0294C7CBA29>102 D<14E0EB03F8A21307A314F0EB01C0
90C7FCAB13F8EA03FEEA070F000E1380121C121812381230EA701F1260133F00E0130012
C05BEA007EA213FE5B1201A25B12035BA20007131813E01438000F133013C01470EB8060
14E014C01381EB838038078700EA03FEEA00F815397EB71D>105
D<150FED3F80A2157FA31600151C92C7FCABEC0F80EC3FE0ECF0F0903801C0F849487E14
005B130E130C131CEB1801133801305BA2EB0003A25DA21407A25DA2140FA25DA2141FA2
5DA2143FA292C7FCA25CA2147EA214FEA25CA21301001E5B123F387F83F0A238FF87E049
5A00FE5BD87C1FC8FCEA707EEA3FF8EA0FC0214981B722>I110 DI<90390F8003F090391FE00FFC903939F0
3C1F903A70F8700F80903AE0FDE007C09038C0FF80030013E00001491303018015F05CEA
038113015CA2D800031407A25CA20107140FA24A14E0A2010F141F17C05CEE3F80131FEE
7F004A137E16FE013F5C6E485A4B5A6E485A90397F700F80DA383FC7FC90387E1FFCEC07
E001FEC9FCA25BA21201A25BA21203A25B1207B512C0A32C3583A42A>I<02FC13C09038
03FF0190380F838390383F01C790397E00EF8049137F485A4848133F000715005B485A00
1F5C157E485AA2007F14FE90C75AA3481301485CA31403485CA314075D140F127C141F00
7E495A003E137F381F01EF380F839F3903FF1F80EA00FC1300143F92C7FCA35C147EA314
FE5C130190387FFFF0A322357DA425>I<14FF010313C090380F80F090383E0038017813
1C153C4913FC0001130113E0A33903F000F06D13007F3801FFE014FC14FF6C14806D13C0
011F13E013039038003FF014071403001E1301127FA24814E0A348EB03C012F800E0EB07
800070EB0F006C133E001E13F83807FFE0000190C7FC1E267CA427>115
DI
E /Ff 46 122 df<011FB512FEA39026001FFEC8FCEC07F8A8EC3FFE0103B512E0D91FF7
13FC90397F07F87F01FCEC1F80D803F8EC0FE0D807F06E7ED80FE06E7E001F82D83FC06E
7EA2007F8201808000FF1780A7007F170001C05C003F5EA2D81FE04A5A000F5ED807F04A
5AD803F84A5AD800FCEC1F80017F027FC7FC90391FF7FFFC0103B512E09026003FFEC8FC
EC07F8A8EC1FFE011FB512FEA331397BB83C>8 D12
D<121C127FEAFF80A213C0A3127F121C1200A412011380A2120313005A1206120E5A5A5A
12600A1979B917>39 D<146014E0EB01C0EB0380EB0700130E131E5B5BA25B485AA2485A
A212075B120F90C7FCA25A121EA2123EA35AA65AB2127CA67EA3121EA2121F7EA27F1207
7F1203A26C7EA26C7E1378A27F7F130E7FEB0380EB01C0EB00E01460135278BD20>I<12
C07E12707E7E7E120F6C7E6C7EA26C7E6C7EA21378A2137C133C133E131EA2131F7FA214
80A3EB07C0A6EB03E0B2EB07C0A6EB0F80A31400A25B131EA2133E133C137C1378A25BA2
485A485AA2485A48C7FC120E5A5A5A5A5A13527CBD20>I<15301578B3A6007FB812F8B9
12FCA26C17F8C80078C8FCB3A6153036367BAF41>43 D<121C127FEAFF80A213C0A3127F
121C1200A412011380A2120313005A1206120E5A5A5A12600A19798817>II<121C127FEAFF80A5EA7F00121C0909798817>I48 DIII<1538A2157815F8A2140114031407A2140F
141F141B14331473146314C313011483EB030313071306130C131C131813301370136013
C01201EA038013005A120E120C5A123812305A12E0B712F8A3C73803F800AB4A7E0103B5
12F8A325397EB82A>I<121C127FEAFF80A5EA7F00121CC7FCB2121C127F5A1380A4127F
121D1201A412031300A25A1206A2120E5A121812385A1260093479A317>59
D<007FB812F8B912FCA3CCFCAEB912FCA36C17F836167B9F41>61
D<913A01FF800180020FEBE003027F13F8903A01FF807E07903A03FC000F0FD90FF0EB03
9F4948EB01DFD93F80EB00FF49C8127F01FE153F12014848151F4848150FA248481507A2
485A1703123F5B007F1601A35B00FF93C7FCAD127F6DED0180A3123F7F001F160318006C
7E5F6C7E17066C6C150E6C6C5D00001618017F15386D6C5CD91FE05C6D6CEB03C0D903FC
EB0F80902701FF803FC7FC9039007FFFFC020F13F002011380313D7BBA3C>67
D69
D76 D78 DI91 D93
D97 DIIII<147E903803FF8090380FC1E0EB1F8790
383F0FF0137EA213FCA23901F803C091C7FCADB512FCA3D801F8C7FCB3AB487E387FFFF8
A31C3B7FBA19>IIII<
EA03F012FFA3120F1203B3B3AD487EB512C0A3123A7EB917>108
D<2703F00FF0EB1FE000FFD93FFCEB7FF8913AF03F01E07E903BF1C01F83803F3D0FF380
0FC7001F802603F70013CE01FE14DC49D907F8EB0FC0A2495CA3495CB3A3486C496CEB1F
E0B500C1B50083B5FCA340257EA445>I<3903F00FF000FFEB3FFCECF03F9039F1C01F80
3A0FF3800FC03803F70013FE496D7EA25BA35BB3A3486C497EB500C1B51280A329257EA4
2E>II<3903F01FE000FFEB7FF89038F1E07E9039F3801F803A07F700
0FC0D803FEEB07E049EB03F04914F849130116FC150016FEA3167FAA16FEA3ED01FCA26D
EB03F816F06D13076DEB0FE001F614C09039F7803F009038F1E07E9038F0FFF8EC1FC091
C8FCAB487EB512C0A328357EA42E>II<3807E01F00FFEB7FC09038E1E3E09038E387
F0380FE707EA03E613EE9038EC03E09038FC0080491300A45BB3A2487EB512F0A31C257E
A421>II<
1318A51338A31378A313F8120112031207001FB5FCB6FCA2D801F8C7FCB215C0A93800FC
011580EB7C03017E13006D5AEB0FFEEB01F81A347FB220>III
III
E /Fg 15 118 df46 D<157815FC14031407141F14FF130F0007B5FCB6FCA2147F13F0EAF800C7FC
B3B3B3A6007FB712FEA52F4E76CD43>49 DI80
D<91260FFF80130791B500F85B010702FF5B011FEDC03F49EDF07F9026FFFC006D5A4801
E0EB0FFD4801800101B5FC4848C87E48488149150F001F824981123F4981007F82A28412
FF84A27FA26D82A27F7F6D93C7FC14C06C13F014FF15F86CECFF8016FC6CEDFFC017F06C
16FC6C16FF6C17C06C836C836D826D82010F821303010082021F16801400030F15C0ED00
7F040714E01600173F050F13F08383A200788200F882A3187FA27EA219E07EA26CEFFFC0
A27F6D4B13806D17006D5D01FC4B5A01FF4B5A02C04A5A02F8EC7FF0903B1FFFC003FFE0
486C90B65AD8FC0393C7FC48C66C14FC48010F14F048D9007F90C8FC3C5479D24B>83
D98 D<913803FFC0023F13FC49B6FC010715C04901817F903A3FFC007FF849486D
7E49486D7E4849130F48496D7E48178048497F18C0488191C7FC4817E0A248815B18F0A2
12FFA490B8FCA318E049CAFCA6127FA27F7EA218E06CEE01F06E14037E6C6DEC07E0A26C
6DEC0FC06C6D141F6C6DEC3F806D6CECFF00D91FFEEB03FE903A0FFFC03FF8010390B55A
010015C0021F49C7FC020113F034387CB63D>101 D<137F497E000313E0487FA2487FA7
6C5BA26C5BC613806DC7FC90C8FCADEB3FF0B5FCA512017EB3B3A6B612E0A51B547BD325
>105 D108
DII<913801FFE0021F13FE91B6
12C0010315F0010F9038807FFC903A1FFC000FFED97FF86D6C7E49486D7F48496D7F4849
6D7F4A147F48834890C86C7EA24883A248486F7EA3007F1880A400FF18C0AC007F1880A3
003F18006D5DA26C5FA26C5F6E147F6C5F6C6D4A5A6C6D495B6C6D495B6D6C495BD93FFE
011F90C7FC903A0FFF807FFC6D90B55A010015C0023F91C8FC020113E03A387CB643>I<
90397FE003FEB590380FFF80033F13E04B13F09238FE1FF89139E1F83FFC0003D9E3E013
FEC6ECC07FECE78014EF150014EE02FEEB3FFC5CEE1FF8EE0FF04A90C7FCA55CB3AAB612
FCA52F367CB537>114 D<143EA6147EA414FEA21301A313031307A2130F131F133F13FF
5A000F90B6FCB8FCA426003FFEC8FCB3A9EE07C0AB011FEC0F8080A26DEC1F0015806DEB
C03E6DEBF0FC6DEBFFF86D6C5B021F5B020313802A4D7ECB34>116
DI E /Fh 19 122 df<121EEA7F8012FF13C0A213E0A3
127FEA1E601200A413E013C0A312011380120313005A1206120E5A5A5A12600B1D78891B
>44 D<143014F013011303131F13FFB5FC13E713071200B3B3B0497E497E007FB6FCA320
4278C131>49 D<000615C0D807C0130701FCEB7F8090B612005D5D5D15E0158026063FFC
C7FC90C9FCAE14FF010713C090381F01F090383800FC01F0137ED807C07F49EB1F8016C0
90C7120F000615E0C8EA07F0A316F81503A216FCA5123E127F487EA416F890C712075A00
6015F0A20070140F003015E00038EC1FC07E001EEC3F806CEC7F006C6C13FE6C6C485A39
01F807F039007FFFE0011F90C7FCEB07F826447BC131>53 D<14FF010713E0011F13F890
387F80FC9038FC007E48487F4848EB1F804848EB0FC0000FEC07E0485AED03F0485A16F8
007F140190C713FCA25AA216FE1500A516FFA46C5CA36C7E5D121F7F000F5C6C6C130615
0E6C6C5B6C6C5BD8007C5B90383F01E090390FFF80FE903801FE0090C8FC150116FCA4ED
03F8A216F0D80F801307486C14E0486C130F16C0ED1F80A249EB3F0049137E001EC75A00
1C495A000F495A3907E01FE06CB51280C649C7FCEB1FF028447CC131>57
D70 D82 D<49B41303010FEBE007013F
13F89039FE00FE0FD801F8131FD807E0EB079F49EB03DF48486DB4FC48C8FC4881003E81
127E82127C00FC81A282A37E82A27EA26C6C91C7FC7F7FEA3FF813FE381FFFE06C13FE6C
EBFFE06C14FC6C14FF6C15C0013F14F0010F80010180D9001F7F14019138001FFF030313
80816F13C0167F163F161F17E000C0150FA31607A37EA36C16C0160F7E17806C151F6C16
006C5D6D147ED8FBC05CD8F9F0495AD8F07C495A90393FC00FE0D8E00FB51280010149C7
FC39C0003FF02B487BC536>I97 DII<167FED3FFFA315018182B3EC7F8090
3803FFF090380FC07C90383F000E017E1307496D5AD803F87F48487F5B000F81485AA248
5AA2127FA290C8FC5AAB7E7FA2123FA26C7EA2000F5D7F6C6C5B00035C6C6C9038077F80
6C6C010E13C0013F011C13FE90380FC0F8903803FFE09026007F0013002F467DC436>I<
EB01FE903807FFC090381F03F090387E00FC49137E48487F485A4848EB1F80000F15C049
130F121F484814E01507A2007F15F090C7FCA25AA390B6FCA290C9FCA67EA27FA2123F16
306C7E1670000F15606D14E06C6C14C0000314016C6CEB03806C6CEB0700013E131E9038
1F80F8903803FFE0010090C7FC242E7DAC2B>I105
D107 D111 D<3903F803F000FFEB1F
FCEC3C3EEC707F0007EBE0FF3803F9C000015B13FBEC007E153C01FF13005BA45BB3A748
B4FCB512FEA3202C7DAB26>114 D<1306A5130EA4131EA3133E137EA213FE1201120700
1FB512F0B6FCA2C648C7FCB3A4150CAA017E131C017F1318A26D133890381F8030ECC070
903807E0E0903801FFC09038007F001E3E7EBC26>116 DI121
D E /Fi 12 118 df68 D77 D<4AB47E020F13F8023F13FE9139FF007F80D9
03FCEB07E0D907F0EB01F0D91FE0EB007849488049488049C87E48485D4915FF00034B13
8048485CA2485AA2485AA2003F6F130049EC007C94C7FC127FA35B12FFAD127F7FA4123F
7FA2001FEE01C07F000F16036D168012076C6C15076D160000015E6C6C151E6D6C5C6D6C
5C6D6C5CD90FF8495AD903FCEB07C0903A00FF803F8091263FFFFEC7FC020F13F8020113
8032417CBF3A>99 D101 D<133C13FF487F487FA66C5B6C90C7FC133C90C8FCB3A2EB03C0EA07FF127F
A41201EA007FA2133FB3B3AC497E497EB612E0A41B5F7DDE23>105
D108 D110
DI<90
39078003F8D807FFEB0FFFB5013F13C092387C0FE0913881F01F9238E03FF00001EB8380
39007F8700148FEB3F8E029CEB1FE0EE0FC00298EB030002B890C7FCA214B014F0A25CA5
5CB3B0497EEBFFF8B612FCA42C3F7CBE33>114 D<9139FFE00180010FEBFC03017FEBFF
073A01FF001FCFD803F8EB03EFD807E0EB01FF48487F4848147F48C8123F003E151F007E
150F127CA200FC1507A316037EA27E7F6C7E6D91C7FC13F8EA3FFE381FFFF06CEBFF806C
14F86C14FF6C15C06C6C14F0011F80010714FED9007F7F02031480DA003F13C015030300
13E0167F00E0ED1FF0160F17F86C15071603A36C1501A37EA26C16F016037E17E06D1407
6DEC0FC06D1580D8FDF0141FD8F8F8EC7F00013E14FC3AF01FC00FF80107B512E0D8E001
148027C0003FF8C7FC2D417DBF34>I<1438A71478A414F8A31301A31303A21307130F13
1FA2137F13FF1203000F90B6FCB8FCA3260007F8C8FCB3AE17E0AE6D6CEB01C0A316036D
6C148016076D6C14006E6C5A91383FC01E91381FF07C6EB45A020313E09138007F802B59
7FD733>II
E end
TeXDict begin

1 0 bop 1226 872 a Fi(Multiuser)45 b(Detection)1509 1112
y Fh(Scott)33 b(Ric)m(k)-5 b(ard)1416 1308 y(F)d(ebruary)33
b(15,)f(1999)-300 1665 y Fg(Solution)46 b(to)f(Problem)g(2.11)-300
1847 y Ff(Let)28 b(us)f(examine)g(the)h(single-user)e(signal)h
(\(Equation)g(2.120\),)846 2111 y Fe(S)5 b Ff(\()p Fe(t)p
Ff(;)14 b Fe(b)p Ff([0])p Fe(;)g(:)g(:)g(:)f(;)h(b)p
Ff([2)p Fe(M)9 b Ff(]\))22 b(=)h Fe(cos)p Ff(\(2)p Fe(\031)s(f)1945
2123 y Fd(c)1978 2111 y Fe(t)c Ff(+)2118 2007 y Fc(2)p
Fd(M)2110 2032 y Fb(X)2116 2209 y Fd(i)p Fc(=0)2243 2111
y Fe(b)p Ff([)p Fe(i)p Ff(]\010\()p Fe(t)g Fa(\000)f
Fe(iT)12 b Ff(\)\))p Fe(;)-300 2371 y Ff(o)n(v)n(er)26
b(the)i(time)g(in)n(terv)-5 b(al)27 b(\(0)p Fe(;)14 b(T)e
Ff(\).)36 b(Ov)n(er)26 b(this)i(in)n(terv)-5 b(al,)27
b(the)h(signal)f(is,)556 2554 y Fe(S)5 b Ff(\()p Fe(t)24
b Fa(2)f Ff(\(0)p Fe(;)14 b(T)e Ff(\)\))82 b(=)h Fe(cos)p
Ff(\(2)p Fe(\031)s(f)1522 2566 y Fd(c)1556 2554 y Fe(t)18
b Ff(+)g Fe(b)p Ff([0]\010\()p Fe(t)p Ff(\)\))1094 2678
y(=)83 b Fe(cos)p Ff(\(2)p Fe(\031)s(f)1522 2690 y Fd(c)1556
2678 y Fe(t)p Ff(\))p Fe(cos)p Ff(\()p Fe(b)p Ff([0]\010\()p
Fe(t)p Ff(\)\))19 b Fa(\000)f Fe(sin)p Ff(\(2)p Fe(\031)s(f)2460
2690 y Fd(c)2493 2678 y Fe(t)p Ff(\))p Fe(sin)p Ff(\()p
Fe(b)p Ff([0]\010\()p Fe(t)p Ff(\)\))1094 2803 y(=)83
b Fe(cos)p Ff(\(2)p Fe(\031)s(f)1522 2815 y Fd(c)1556
2803 y Fe(t)p Ff(\))p Fe(cos)p Ff(\(\010\()p Fe(t)p Ff(\)\))19
b Fa(\000)f Fe(sin)p Ff(\(2)p Fe(\031)s(f)2336 2815 y
Fd(c)2369 2803 y Fe(t)p Ff(\))p Fe(b)p Ff([0])p Fe(sin)p
Ff(\(\010\()p Fe(t)p Ff(\)\))1094 2927 y(=)83 b Fe(cos)p
Ff(\(2)p Fe(\031)s(f)1522 2939 y Fd(c)1556 2927 y Fe(t)p
Ff(\))p Fe(cos)p Ff(\(\010\()p Fe(t)p Ff(\)\))19 b(+)f
Fe(sin)p Ff(\(2)p Fe(\031)s(f)2336 2939 y Fd(c)2369 2927
y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p Ff([0]\))p Fe(sin)p
Ff(\(\010\()p Fe(t)p Ff(\)\))p Fe(;)-300 3110 y Ff(where)27
b(w)n(e)g(ha)n(v)n(e)g(made)g(use)h(of)f(the)h(trigonometric)e(iden)n
(tit)n(y)-7 b(,)1023 3293 y Fe(cos)p Ff(\()p Fe(\013)19
b Ff(+)f Fe(\014)t Ff(\))24 b(=)f Fe(cos)p Ff(\()p Fe(\013)p
Ff(\))p Fe(cos)p Ff(\()p Fe(\014)t Ff(\))d Fa(\000)e
Fe(sin)p Ff(\()p Fe(\013)p Ff(\))p Fe(sin)p Ff(\()p Fe(\014)t
Ff(\))p Fe(;)-300 3475 y Ff(and)27 b(the)h(fact)g(that)g
Fe(b)p Ff([0])22 b Fa(2)i(f\000)p Ff(1)p Fe(;)14 b Ff(1)p
Fa(g)25 b Ff(in)j(order)e(to)i(eliminate)f Fe(b)p Ff([0])g(from)g(the)h
(cosine)f(and)h(pull)g(it)g(out)f(from)h(the)g(sine.)-175
3575 y(Ov)n(er)e(the)i(in)n(terv)-5 b(al)27 b(\()p Fe(T)7
b(;)14 b Ff(2)p Fe(T)e Ff(\),)26 b(the)i(signal)f(is,)96
3757 y Fe(S)5 b Ff(\()p Fe(t)23 b Fa(2)h Ff(\()p Fe(T)7
b(;)14 b Ff(2)p Fe(T)e Ff(\)\))81 b(=)i Fe(cos)p Ff(\(2)p
Fe(\031)s(f)1117 3769 y Fd(c)1151 3757 y Fe(t)18 b Ff(+)g
Fe(b)p Ff([0])1416 3725 y Fd(\031)p 1415 3739 41 4 v
1419 3786 a Fc(2)1485 3757 y Ff(+)g Fe(b)p Ff([1]\010\()p
Fe(t)g Fa(\000)g Fe(T)12 b Ff(\)\))689 3882 y(=)83 b
Fe(cos)p Ff(\(2)p Fe(\031)s(f)1117 3894 y Fd(c)1151 3882
y Fe(t)p Ff(\))p Fe(cos)p Ff(\()p Fe(b)p Ff([0])1494
3849 y Fd(\031)p 1493 3863 V 1497 3911 a Fc(2)1563 3882
y Ff(+)18 b Fe(b)p Ff([1]\010\()p Fe(t)g Fa(\000)g Fe(T)12
b Ff(\)\))18 b Fa(\000)g Fe(sin)p Ff(\(2)p Fe(\031)s(f)2502
3894 y Fd(c)2535 3882 y Fe(t)p Ff(\))p Fe(sin)p Ff(\()p
Fe(b)p Ff([0])2881 3849 y Fd(\031)p 2880 3863 V 2884
3911 a Fc(2)2949 3882 y Ff(+)g Fe(b)p Ff([1]\010\()p
Fe(t)g Fa(\000)g Fe(T)12 b Ff(\)\))689 4007 y(=)83 b
Fe(cos)p Ff(\(2)p Fe(\031)s(f)1117 4019 y Fd(c)1151 4007
y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p Ff([0]\))p Fe(sin)p
Ff(\()p Fe(b)p Ff([1]\010\()p Fe(t)17 b Fa(\000)h Fe(T)12
b Ff(\)\))18 b Fa(\000)g Fe(sin)p Ff(\(2)p Fe(\031)s(f)2471
4019 y Fd(c)2504 4007 y Fe(t)p Ff(\)\()p Fe(b)p Ff([0]\))p
Fe(cos)p Ff(\()p Fe(b)p Ff([1]\010\()p Fe(t)g Fa(\000)g
Fe(T)12 b Ff(\)\))689 4131 y(=)83 b Fe(cos)p Ff(\(2)p
Fe(\031)s(f)1117 4143 y Fd(c)1151 4131 y Fe(t)p Ff(\)\()p
Fa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1]\))p Fe(sin)p
Ff(\(\010\()p Fe(t)17 b Fa(\000)h Fe(T)12 b Ff(\)\))18
b Fa(\000)g Fe(sin)p Ff(\(2)p Fe(\031)s(f)2471 4143 y
Fd(c)2504 4131 y Fe(t)p Ff(\)\()p Fe(b)p Ff([0]\))p Fe(cos)p
Ff(\(\010\()p Fe(t)h Fa(\000)f Fe(T)12 b Ff(\)\))689
4256 y(=)83 b Fe(cos)p Ff(\(2)p Fe(\031)s(f)1117 4268
y Fd(c)1151 4256 y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p
Ff([0])p Fe(b)p Ff([1]\))p Fe(sin)p Ff(\(\010\()p Fe(t)17
b Fa(\000)h Fe(T)12 b Ff(\)\))18 b(+)g Fe(sin)p Ff(\(2)p
Fe(\031)s(f)2471 4268 y Fd(c)2504 4256 y Fe(t)p Ff(\)\()p
Fa(\000)p Fe(b)p Ff([0]\))p Fe(cos)p Ff(\(\010\()p Fe(t)h
Fa(\000)f Fe(T)12 b Ff(\)\))p Fe(;)-300 4438 y Ff(where)27
b(w)n(e)g(ha)n(v)n(e)g(made)g(use)h(of)f(the)h(trigonometric)e(iden)n
(tities,)1287 4621 y Fe(cos)p Ff(\()p Fe(\013)19 b Ff(+)f
Fe(b)p Ff([)p Fe(i)p Ff(])1710 4588 y Fd(\031)p 1709
4602 V 1713 4650 a Fc(2)1760 4621 y Ff(\))23 b(=)g Fa(\000)p
Fe(b)p Ff([)p Fe(i)p Ff(])p Fe(sin)p Ff(\()p Fe(\013)p
Ff(\))1307 4804 y Fe(sin)p Ff(\()p Fe(\013)c Ff(+)f Fe(b)p
Ff([)p Fe(i)p Ff(])1733 4771 y Fd(\031)p 1732 4785 V
1736 4832 a Fc(2)1783 4804 y Ff(\))23 b(=)g Fe(b)p Ff([)p
Fe(i)p Ff(])p Fe(cos)p Ff(\()p Fe(\013)p Ff(\))p Fe(:)1779
5255 y Ff(1)p eop
2 1 bop -300 523 a Ff(Con)n(tin)n(uing)27 b(in)h(this)g(fashion,)-255
706 y Fe(S)5 b Ff(\()p Fe(t)23 b Fa(2)g Ff(\(2)p Fe(T)7
b(;)14 b Ff(3)p Fe(T)e Ff(\)\))81 b(=)i Fe(cos)p Ff(\(2)p
Fe(\031)s(f)807 718 y Fd(c)841 706 y Fe(t)18 b Ff(+)g(\()p
Fe(b)p Ff([0])g(+)g Fe(b)p Ff([1]\))1395 673 y Fd(\031)p
1395 687 41 4 v 1399 734 a Fc(2)1464 706 y Ff(+)g Fe(b)p
Ff([2]\010\()p Fe(t)g Fa(\000)g Ff(2)p Fe(T)12 b Ff(\)\))379
830 y(=)83 b Fe(cos)p Ff(\(2)p Fe(\031)s(f)807 842 y
Fd(c)841 830 y Fe(t)p Ff(\))p Fe(cos)p Ff(\(\()p Fe(b)p
Ff([0])18 b(+)g Fe(b)p Ff([1]\))1473 798 y Fd(\031)p
1473 812 V 1477 859 a Fc(2)1542 830 y Ff(+)g Fe(b)p Ff([2]\010\()p
Fe(t)g Fa(\000)g Ff(2)p Fe(T)12 b Ff(\)\))18 b Fa(\000)g
Fe(sin)p Ff(\(2)p Fe(\031)s(f)2523 842 y Fd(c)2556 830
y Fe(t)p Ff(\))p Fe(sin)p Ff(\(\()p Fe(b)p Ff([0])f(+)h
Fe(b)p Ff([1]\))3190 798 y Fd(\031)p 3190 812 V 3194
859 a Fc(2)3259 830 y Ff(+)g Fe(b)p Ff([2]\010\()p Fe(t)g
Fa(\000)g Ff(2)p Fe(T)12 b Ff(\)\))379 955 y(=)83 b Fe(cos)p
Ff(\(2)p Fe(\031)s(f)807 967 y Fd(c)841 955 y Fe(t)p
Ff(\)\()p Fa(\000)p Fe(b)p Ff([0]\))p Fe(sin)p Ff(\()p
Fe(b)p Ff([1])1440 922 y Fd(\031)p 1438 936 V 1442 983
a Fc(2)1507 955 y Ff(+)18 b Fe(b)p Ff([2]\010\()p Fe(t)g
Fa(\000)g Ff(2)p Fe(T)12 b Ff(\)\))18 b Fa(\000)g Fe(sin)p
Ff(\(2)p Fe(\031)s(f)2488 967 y Fd(c)2521 955 y Fe(t)p
Ff(\)\()p Fe(b)p Ff([0]\))p Fe(cos)p Ff(\()p Fe(b)p Ff([1])3052
922 y Fd(\031)p 3052 936 V 3056 983 a Fc(2)3121 955 y
Ff(+)g Fe(b)p Ff([2]\010\()p Fe(t)g Fa(\000)g Ff(2)p
Fe(T)12 b Ff(\)\))379 1079 y(=)83 b Fe(cos)p Ff(\(2)p
Fe(\031)s(f)807 1091 y Fd(c)841 1079 y Fe(t)p Ff(\)\()p
Fa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1]\))p Fe(cos)p
Ff(\()p Fe(b)p Ff([2]\010\()p Fe(t)17 b Fa(\000)h Ff(2)p
Fe(T)12 b Ff(\)\))17 b Fa(\000)h Fe(sin)p Ff(\(2)p Fe(\031)s(f)2323
1091 y Fd(c)2356 1079 y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p
Ff([0])p Fe(b)p Ff([1]\))p Fe(sin)p Ff(\()p Fe(b)p Ff([2]\010\()p
Fe(t)f Fa(\000)h Ff(2)p Fe(T)12 b Ff(\)\))379 1204 y(=)83
b Fe(cos)p Ff(\(2)p Fe(\031)s(f)807 1216 y Fd(c)841 1204
y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1]\))p
Fe(cos)p Ff(\(\010\()p Fe(t)18 b Fa(\000)g Ff(2)p Fe(T)12
b Ff(\)\))17 b Fa(\000)h Fe(sin)p Ff(\(2)p Fe(\031)s(f)2200
1216 y Fd(c)2233 1204 y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p
Ff([0])p Fe(b)p Ff([1])p Fe(b)p Ff([2]\))p Fe(sin)p Ff(\(\010\()p
Fe(t)f Fa(\000)h Ff(2)p Fe(T)12 b Ff(\)\))379 1328 y(=)83
b Fe(cos)p Ff(\(2)p Fe(\031)s(f)807 1340 y Fd(c)841 1328
y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1]\))p
Fe(cos)p Ff(\(\010\()p Fe(t)18 b Fa(\000)g Ff(2)p Fe(T)12
b Ff(\)\))17 b(+)h Fe(sin)p Ff(\(2)p Fe(\031)s(f)2200
1340 y Fd(c)2233 1328 y Fe(t)p Ff(\)\()p Fe(b)p Ff([0])p
Fe(b)p Ff([1])p Fe(b)p Ff([2]\))p Fe(sin)p Ff(\(\010\()p
Fe(t)f Fa(\000)h Ff(2)p Fe(T)12 b Ff(\)\))p Fe(;)-300
1511 y Ff(and)27 b(one)h(last)f(time,)-300 1694 y Fe(S)5
b Ff(\()p Fe(t)23 b Fa(2)g Ff(\(3)p Fe(T)7 b(;)14 b Ff(4)p
Fe(T)e Ff(\)\))82 b(=)g Fe(cos)p Ff(\(2)p Fe(\031)s(f)762
1706 y Fd(c)796 1694 y Fe(t)18 b Ff(+)g(\()p Fe(b)p Ff([0])g(+)g
Fe(b)p Ff([1])g(+)g Fe(b)p Ff([2]\))1575 1661 y Fd(\031)p
1575 1675 V 1579 1722 a Fc(2)1644 1694 y Ff(+)g Fe(b)p
Ff([3]\010\()p Fe(t)g Fa(\000)g Ff(3)p Fe(T)12 b Ff(\)\))335
1818 y(=)82 b Fe(cos)p Ff(\(2)p Fe(\031)s(f)762 1830
y Fd(c)796 1818 y Fe(t)p Ff(\))p Fe(cos)p Ff(\(\()p Fe(b)p
Ff([0])19 b(+)f Fe(b)p Ff([1])f(+)h Fe(b)p Ff([2]\))1653
1785 y Fd(\031)p 1653 1799 V 1657 1847 a Fc(2)1722 1818
y Ff(+)g Fe(b)p Ff([3]\010\()p Fe(t)g Fa(\000)g Ff(3)p
Fe(T)12 b Ff(\)\))18 b Fa(\000)g Fe(sin)p Ff(\(2)p Fe(\031)s(f)2703
1830 y Fd(c)2736 1818 y Fe(t)p Ff(\))p Fe(sin)p Ff(\(\()p
Fe(b)p Ff([0])g(+)g Fe(b)p Ff([1])f(+)h Fe(b)p Ff([2]\))3595
1785 y Fd(\031)p 3595 1799 V 3599 1847 a Fc(2)3664 1818
y Ff(+)g Fe(b)p Ff([3]\010\()p Fe(t)g Fa(\000)g Ff(3)p
Fe(T)12 b Ff(\)\))335 1943 y(=)82 b Fe(cos)p Ff(\(2)p
Fe(\031)s(f)762 1955 y Fd(c)796 1943 y Fe(t)p Ff(\)\()p
Fa(\000)p Fe(b)p Ff([0]\))p Fe(sin)p Ff(\(\()p Fe(b)p
Ff([1])17 b(+)h Fe(b)p Ff([2]\))1683 1910 y Fd(\031)p
1683 1924 V 1687 1971 a Fc(2)1752 1943 y Ff(+)g Fe(b)p
Ff([3]\010\()p Fe(t)g Fa(\000)g Ff(3)p Fe(T)12 b Ff(\)\))18
b Fa(\000)g Fe(sin)p Ff(\(2)p Fe(\031)s(f)2733 1955 y
Fd(c)2766 1943 y Fe(t)p Ff(\)\()p Fe(b)p Ff([0]\))p Fe(cos)p
Ff(\(\()p Fe(b)p Ff([1])g(+)g Fe(b)p Ff([2]\))3586 1910
y Fd(\031)p 3586 1924 V 3590 1971 a Fc(2)3655 1943 y
Ff(+)g Fe(b)p Ff([3]\010\()p Fe(t)g Fa(\000)g Ff(3)p
Fe(T)12 b Ff(\)\))335 2067 y(=)82 b Fe(cos)p Ff(\(2)p
Fe(\031)s(f)762 2079 y Fd(c)796 2067 y Fe(t)p Ff(\)\()p
Fa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1]\))p Fe(cos)p
Ff(\()p Fe(b)p Ff([2])1516 2035 y Fd(\031)p 1515 2049
V 1519 2096 a Fc(2)1584 2067 y Ff(+)18 b Fe(b)p Ff([3]\010\()p
Fe(t)g Fa(\000)g Ff(3)p Fe(T)12 b Ff(\)\))17 b Fa(\000)h
Fe(sin)p Ff(\(2)p Fe(\031)s(f)2564 2079 y Fd(c)2597 2067
y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1]\))p
Fe(sin)p Ff(\()p Fe(b)p Ff([2])3320 2035 y Fd(\031)p
3318 2049 V 3322 2096 a Fc(2)3387 2067 y Ff(+)g Fe(b)p
Ff([3]\010\()p Fe(t)g Fa(\000)g Ff(3)p Fe(T)12 b Ff(\)\))335
2192 y(=)82 b Fe(cos)p Ff(\(2)p Fe(\031)s(f)762 2204
y Fd(c)796 2192 y Fe(t)p Ff(\)\()p Fe(b)p Ff([0])p Fe(b)p
Ff([1])p Fe(b)p Ff([2]\))p Fe(sin)p Ff(\()p Fe(b)p Ff([3]\010\()p
Fe(t)16 b Fa(\000)i Ff(3)p Fe(T)12 b Ff(\)\))18 b Fa(\000)g
Fe(sin)p Ff(\(2)p Fe(\031)s(f)2340 2204 y Fd(c)2373 2192
y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1])p
Fe(b)p Ff([2]\))p Fe(cos)p Ff(\()p Fe(b)p Ff([3]\010\()p
Fe(t)e Fa(\000)i Ff(3)p Fe(T)12 b Ff(\)\))335 2316 y(=)82
b Fe(cos)p Ff(\(2)p Fe(\031)s(f)762 2328 y Fd(c)796 2316
y Fe(t)p Ff(\)\()p Fe(b)p Ff([0])p Fe(b)p Ff([1])p Fe(b)p
Ff([2])p Fe(b)p Ff([3]\))p Fe(sin)p Ff(\(\010\()p Fe(t)16
b Fa(\000)i Ff(3)p Fe(T)12 b Ff(\)\))18 b Fa(\000)g Fe(sin)p
Ff(\(2)p Fe(\031)s(f)2340 2328 y Fd(c)2373 2316 y Fe(t)p
Ff(\)\()p Fa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1])p Fe(b)p
Ff([2]\))p Fe(cos)p Ff(\(\010\()p Fe(t)f Fa(\000)h Ff(3)p
Fe(T)12 b Ff(\)\))335 2441 y(=)82 b Fe(cos)p Ff(\(2)p
Fe(\031)s(f)762 2453 y Fd(c)796 2441 y Fe(t)p Ff(\)\()p
Fe(b)p Ff([0])p Fe(b)p Ff([1])p Fe(b)p Ff([2])p Fe(b)p
Ff([3]\))p Fe(sin)p Ff(\(\010\()p Fe(t)16 b Fa(\000)i
Ff(3)p Fe(T)12 b Ff(\)\))18 b(+)g Fe(sin)p Ff(\(2)p Fe(\031)s(f)2340
2453 y Fd(c)2373 2441 y Fe(t)p Ff(\)\()p Fe(b)p Ff([0])p
Fe(b)p Ff([1])p Fe(b)p Ff([2]\))p Fe(cos)p Ff(\(\010\()p
Fe(t)f Fa(\000)h Ff(3)p Fe(T)12 b Ff(\)\))p Fe(:)-300
2623 y Ff(No)n(w,)34 b(grouping)e(the)h(terms)g(from)g(the)g(end)g(of)g
(eac)n(h)g(calculation)f(and)h(noting)g(that)g(the)g
Fe(cos)g Fa(!)f(\000)p Fe(sin)f Fa(!)h(\000)p Fe(cos)g
Fa(!)g Fe(sin)h Ff(tran-)-300 2723 y(sitions)j(created)f(b)n(y)h
(iterativ)n(ely)f(pulling)i(out)f Fe(b)p Ff([)p Fe(i)p
Ff(])1357 2690 y Fd(\031)p 1356 2704 V 1360 2752 a Fc(2)1443
2723 y Ff(terms)g(accoun)n(t)g(for)f(the)i(p)r(erio)r(dic)f
(de\014nition)g(of)h Fa(f)p Fe(q)s Ff([0])p Fe(;)14 b(q)s
Ff([1])p Fe(;)g(q)s Ff([2])p Fe(;)g(q)s Ff([3])p Fa(g)34
b Ff(=)-300 2823 y Fa(f)p Ff(1)p Fe(;)14 b Fa(\000)p
Ff(1)p Fe(;)g Fa(\000)p Ff(1)p Fe(;)g Ff(1)p Fa(g)p Ff(,)21
b(w)n(e)j(calculate)f(that)i(the)f(single-user)f(system)h(can)g(b)r(e)g
(expressed)g(as)f(the)i(follo)n(wing)e(t)n(w)n(o-user)f(system)i(where)
g(eac)n(h)-300 2922 y(user's)j(signature)f(w)n(a)n(v)n(eform)g(has)h
(duration)g(2)p Fe(T)12 b Ff(,)548 3182 y Fe(S)5 b Ff(\()p
Fe(t)p Ff(;)14 b Fe(b)p Ff([0])p Fe(;)g(:)g(:)g(:)e(;)i(b)p
Ff([2)p Fe(M)9 b Ff(]\))22 b(=)1391 3078 y Fd(M)1366
3103 y Fb(X)1372 3280 y Fd(i)p Fc(=0)1500 3182 y Fe(d)p
Ff([2)p Fe(i)p Ff(])p Fe(s)1699 3194 y Fc(1)1735 3182
y Ff(\()p Fe(t)d Fa(\000)f Ff(2)p Fe(iT)12 b Ff(\))17
b(+)h Fe(d)p Ff([2)p Fe(i)g Ff(+)g(1])p Fe(s)2505 3194
y Fc(2)2542 3182 y Ff(\()p Fe(t)g Fa(\000)g Ff(2)p Fe(iT)29
b Fa(\000)18 b Fe(T)12 b Ff(\))o Fe(;)-300 3437 y Ff(where,)816
3536 y Fe(s)855 3548 y Fc(1)892 3536 y Ff(\()p Fe(t)p
Ff(\))24 b(=)f Fe(sin)p Ff(\(2)p Fe(\031)s(f)1381 3548
y Fd(c)1414 3536 y Fe(t)p Ff(\)[)p Fe(p)p Ff(\()p Fe(t)p
Ff(\))p Fe(sin)p Ff(\010\()p Fe(t)p Ff(\))c(+)f Fe(p)p
Ff(\()p Fe(t)g Fa(\000)g Fe(T)12 b Ff(\))p Fe(cos)p Ff(\010\()p
Fe(t)18 b Fa(\000)g Fe(T)12 b Ff(\)])p Fe(;)817 3686
y(s)856 3698 y Fc(2)894 3686 y Ff(\()p Fe(t)p Ff(\))23
b(=)g Fe(cos)p Ff(\(2)p Fe(\031)s(f)1379 3698 y Fd(c)1412
3686 y Fe(t)p Ff(\)[)p Fe(p)p Ff(\()p Fe(t)p Ff(\))p
Fe(sin)p Ff(\010\()p Fe(t)p Ff(\))c(+)f Fe(p)p Ff(\()p
Fe(t)h Fa(\000)f Fe(T)12 b Ff(\))p Fe(cos)p Ff(\010\()p
Fe(t)18 b Fa(\000)g Fe(T)12 b Ff(\)])p Fe(;)1414 3915
y(d)p Ff([)p Fe(i)p Ff(])23 b(=)f Fe(q)s Ff([)p Fe(i)c
Ff(+)g(1])1960 3812 y Fd(i)1918 3836 y Fb(Y)1914 4013
y Fd(j)s Fc(=0)2043 3915 y Fe(b)p Ff([)p Fe(j)5 b Ff(])p
Fe(:)1779 5255 y Ff(2)p eop end
userdict /end-hook known{end-hook}if