{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "_cstyle1" -1 204 "Times" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "_pstyle 1" -1 200 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "_pstyle2" -1 201 1 {CSTYLE "" -1 -1 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "_pstyle3" -1 202 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 200 "" 0 "" {TEXT 204 3 "01." }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 468 "FFT1:=proc(liste)\nlocal n,zeta,fullis te,even,odd,phi,psi,tab1,tab2,i;\nn:=nops(liste);\nif n=1 \n then lis te\n else zeta:=exp(2*Pi*I/n);\n fulliste:=liste;\n odd:= [seq(fulliste[2*i],i=1..iquo(n,2))];\n even:=[seq(fulliste[2*i+1 ],i=0..iquo(n,2)-1)];\n phi:=FFT1(even);\n psi:=FFT1(odd); \n tab1:=[seq(phi[i]+zeta^(i-1)*psi[i],i=1..n/2)];\n tab2: =[seq(phi[i]+zeta^(n/2+i-1)*psi[i],i=1..n/2)];\n [op(tab1),op(ta b2)];\nend if;\nend proc:" }}}{EXCHG {PARA 200 "" 0 "" {TEXT 204 3 "02 ." }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 38 "IFFT1:=liste->ifft(l iste)/nops(liste):" }}}{EXCHG {PARA 200 "" 0 "" {TEXT 204 3 "03." }}} {EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 469 "ifft:=proc(liste)\nlocal \+ n,zeta,fulliste,even,odd,phi,psi,tab1,tab2,i;\nn:=nops(liste);\nif n=1 \n then liste\n else zeta:=exp(-2*Pi*I/n);\n fulliste:=liste; \n odd:=[seq(fulliste[2*i],i=1..iquo(n,2))];\n even:=[seq( fulliste[2*i+1],i=0..iquo(n,2)-1)];\n phi:=ifft(even);\n p si:=ifft(odd);\n tab1:=[seq(phi[i]+zeta^(i-1)*psi[i],i=1..n/2)]; \n tab2:=[seq(phi[i]+zeta^(n/2+i-1)*psi[i],i=1..n/2)];\n [ op(tab1),op(tab2)];\nend if;\nend proc:" }}}{EXCHG {PARA 200 "" 0 "" {TEXT 204 3 "04." }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 24 "alist :=[seq(k,k=1..16)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alistG72\"\" \"\"\"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*\"#5\"#6\"#7\"#8\"#9\"#:\"#; " }}}{EXCHG {PARA 200 "" 0 "" {TEXT 204 3 "05." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 24 "fft:=evalf(FFT1(alist));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$fftG72$\"$O\"\"\"!^$$!+(*******z!\"*$!+%fr=-%!\")^$$ !+++++!)F,$!+]3PJ>F/^$$!+0+++!)F,$!+4YG(>\"F/^$$!+c******zF,$!+g****** zF,^$$!+x******zF,$!+<\"HaM&F,^$$!+#)******zF,$!+.&3PJ$F,^$$!+t******z F,$!*&*)H\"f\"F/^$$!*++++)F/$!+[N.Hu!#<^$$!+D+++!)F,$\"*&*)H\"f\"F/^$$ !+7+++!)F,$\"+/&3PJ$F,^$$!+/+++!)F,$\"+8\"HaM&F,^$$!+s******zF,$\"+g** ****zF,^$$!+K+++!)F,$\"+3YG(>\"F/^$$!+I+++!)F,$\"+\\3PJ>F/^$$!+[+++!)F ,$\"+\"fr=-%F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "06." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "07." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalf(IFFT1(ff t));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#72^$$\"+,+++5!\"*$!+pf9$R)!#=^ $$\"+-+++?F'$!+JW[@oF*^$$\"+++++IF'$!+YIW?^F*^$$\"+++++SF'$!+:HpCEF*^$ $\"+2+++]F'$\"*gWZX&F*^$$\"+********fF'$\"+G_B$R(F*^$$\"+)*******pF'$ \"+qxl.?F*^$$\"+)*******zF'$\"+N]WT6!#<^$$\"+4+++!*F'$!+KoQqiF*^$$F&! \")$\"+S_c=GF*^$$\"+*******4\"FV$!+s&*[3%)F*^$$\"+++++7FV$\"+XU'3F&F*^ $$\"+++++8FV$!+E2!4F\"FN^$$\"+++++9FV$\"+(>\")fu#F*^$$\"+)******\\\"FV $!+R!fKb\"FN^$$\"+)******f\"FV$\")eTb')F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "08." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "fft:=FFT 1(alist);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$fftG72\"$O\",(^$!\")F) \"\"\"*&F(F*,&*&\"\"#!\"\"F.#F*F.F**&^#F0F*F.F0F*F*F**&-%$expG6#*&^##F *\"\")F*%#PiGF*F*,&F(F*F+F*F*F*,(F:F/*&F:F*)F,F.F*F/*&)F4F.F*,&F:F/*&F :F*F?F*F/F*F*,(^$F)F:F**&FEF*)F,\"\"$F*F**&)F4FHF*,&FEF*FFF*F*F*,(\"#G F**&\"#OF*)F,\"\"%F*F**&)F4FQF*,&\"#KF**&\"#SF*FPF*F*F*F*,(F(F**&F(F*) F,\"\"&F*F**&)F4FenF*,&F(F*FYF*F*F*,(F:F/*&F:F*)F,\"\"'F*F/*&)F4F\\oF* ,&F:F/*&F:F*F[oF*F/F*F*,(FEF**&FEF*)F,\"\"(F*F**&)F4FdoF*,&FEF*FboF*F* F*,&\"#kF**&\"#sF*)F4F:F*F*,(F(F*F+F**&)F4\"\"*F*F " 0 "" {MPLTEXT 1 0 21 "simplify(IFFT1 (fft));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#72\"\"\"\"\"#\"\"$\"\"%\"\" &\"\"'\"\"(\"\")\"\"*\"#5\"#6\"#7\"#8\"#9\"#:\"#;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 202 "" 0 "" {TEXT -1 0 "" }}} {MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }