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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}
{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra
ce have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "Digits:=20;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'Dig
itsG\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 31 "Transform\351e de Fourier discr\350te" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 270 "TFD:=proc(n,y)\n#option trace;\nlocal i,j,M,w,Y;\n
w:=exp(2*I*Pi/n);\nM:=matrix(n,n,0);\nY:=vector(n,0);\n\nfor i from 1 \+
to n do\n  M[i,1]:=1;\n  M[i,2]:=w^(1-i);\n  for j from 3 to n do\n   \+
 M[i,j]:= (M[i,2]^(j-1));\n  od;\nod;\n\nY:=evalf(multiply(M,y));\nRET
URN(evalm(evalf(Y)));\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "a:=[7
,5,6,9,4,5,6,2]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "TFD(8,a);\ntime
(TFD(8,a));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7*$\"#W\"\"
!^$$!53nKeIouu\\>!#>$!57nKeIouu\\\\F-^$$!5+++++++++5F-$\"5+++++++++5F-
^$$\"54nKeIouu\\zF-$!54nKeIouu\\\\F-^$$\"5+++++++++?F-$F)F)^$F6$\"52nK
eIouu\\\\F-^$F1F1^$$!56nKeIouu\\>F-$\"56nKeIouu\\\\F-" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#$\"\"*!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 273 "iTFD:=proc(n,y)\n#option trace;\nl
ocal i,j,M,w,Y;\nw:=exp(2*I*Pi/n);\nM:=matrix(n,n,0);\nY:=vector(n,0);
\n\nfor i from 1 to n do\n  M[i,1]:=1;\n  M[i,2]:=w^(i-1);\n  for j fr
om 3 to n do\n    M[i,j]:= (M[i,2]^(j-1));\n  od;\nod;\n\nY:=evalf(mul
tiply(M,y));\nRETURN(evalm(evalf(Y/n)));\nend:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 351 
"b:=[44., -1.9497474683058326708-4.9497474683058326712*I, -1.000000000
0000000000+1.0000000000000000000*I, 7.9497474683058326709-4.9497474683
058326709*I, 2.0000000000000000000+0.*I, 7.9497474683058326709+4.94974
74683058326707*I, -1.0000000000000000000-1.0000000000000000000*I, -1.9
497474683058326711+4.9497474683058326711*I];\niTFD(8,b);\ntime(iTFD(8,
b));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"bG7*$\"#W\"\"!^$$!53nKeIou
u\\>!#>$!57nKeIouu\\\\F,^$$!5+++++++++5F,$\"5+++++++++5F,^$$\"54nKeIou
u\\zF,$!54nKeIouu\\\\F,^$$\"5+++++++++?F,$F(F(^$F5$\"52nKeIouu\\\\F,^$
F0F0^$$!56nKeIouu\\>F,$\"56nKeIouu\\\\F," }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#-%'vectorG6#7*^$$\"5+++++++++q!#>$!5++++++++]P!#R^$$\"5,++++++++
]F*$\"5++++++++]7F-^$$\"5+++++++++gF*$!5++++++++]7F-^$$\"5+++++++++!*F
*$\"5++++++++]PF-^$$\"5+++++++++SF*$\"5+++++++++]F-^$$\"5*************
*****\\F*$!5+++++++++DF-^$$\"5******************fF*F6^$$\"5+++++++++?F
*F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"*!\"$" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 29 "Tr
ansform\351e de Fourier rapide" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 421 "TFR:=proc(n,w,y)\n#option trace;\nlocal X,Y,T,m,k,b,c,B,C,w2,wk
;\nY:=array(1..n);\n\nif n=1 then Y[1]:=y[1];\nelse m:= iquo(n,2);\n  \+
b:=array(1..m);c:=array(1..m);\n  for k from 1 to m do \n    b[k]:=y[2
*k-1];\n    c[k]:=y[2*k]\n  od;\n  w2:=w*w;\n  B:=TFR(m,w2,b);\n  C:=T
FR(m,w2,c);\n   wk:=1;\n  for k from 1 to m do\n    X:=B[k];\n    T:=w
k*C[k];\n    Y[k]:=evalf((X+T));\n    Y[k+m]:=evalf((X-T));\n    wk:=w
k*w;\n  od;\nfi;\nevalm(Y);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "a:=[7,5
,6,9,4,5,6,2]:\nw:=exp(I*Pi/4);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "
TFR(8,w,a);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG,&*$-%%sqrtG6#
\"\"#\"\"\"#F+F**&^#F,F+F'F+F+" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%'v
ectorG6#7*$\"#W\"\"!^$$!53nKeIouu\\>!#>$\"53nKeIouu\\\\F-^$$!\"\"F)$!5
+++++++++5F-^$$\"53nKeIouu\\zF-F.$\"\"#F)^$F6$!53nKeIouu\\\\F-^$F1$\"5
+++++++++5F-^$F+F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "?FFT" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "x := array(a):\ny := array
([0,0,0,0,0,0,0,0]):\nFFT(3,x,y);\nprint(x);print(y);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vector
G6#7*\"#W$!53nKeIouu\\>!#>$!\"\"\"\"!$\"53nKeIouu\\zF*\"\"#F.F+F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7*\"\"!$!53nKeIouu\\\\!#>$
\"\"\"F'F(F'$\"53nKeIouu\\\\F*$!\"\"F'F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "TFR(4,w,[7.,5.,6.,9.]);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'vectorG6#7&$\"#F\"\"!^$$!5w4!>YZ7F%G=!#>$!5w4!>YZ7F%
GGF-$!\"\"F)^$$\"5w4!>YZ7F%GQF-$\"5w4!>YZ7F%GGF-" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}}}{MARK "4 3 0 0" 22 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
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