{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 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 "Warni ng" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 1056 "#showing how to do FFT and IFT in maple 10 . Nasser Abbasi.\nrestart;\nwith(inttrans):\nwith(LinearAlgebra):\nwit h(plots):\nN:=100:\n\n#the function to fft\ny:= t->sin(t) + 2*sin(3*t) :\n\nlinspace:=proc(fromP,toP,n)\n local incr,data,i,T,L;\n \+ incr:=(toP-fromP)/(n-1);\n L:=Vector(1..n,[]);\n \+ T:=fromP;\n for i from 1 to n do\n L[i]:=T; \n T:=T+incr;\n end do: \n return(L);\n end proc:\n\ndata:=Vector(1..N,[]):\ng:=Vector(1..N,[]):\nT:=linspace( -Pi,Pi,N):\n\nfor i from 1 to N do\n data[i]:=evalf(y(T[i]));\nend \+ do: \n\nY:=DiscreteTransforms:-FourierTransform( data,algorithm=DFT,pa dding=0 ):\nadj:=evalf(sqrt(1/N)): #adjust as maple has normalization \+ factor\nY:=Y/adj:\n\ndt:=T[2]-T[1]:\nfs:=1/dt:\nw:=evalf(linspace(0,fs ,N)):\ns:=[seq(exp(-w[i]),i=1..N)]:\ng:=Vector(N,zip((x,y)->x*y,s,conv ert(Y,list))):\nh:=DiscreteTransforms:-InverseFourierTransform( g ):\n h:=h*sqrt(1/N):#adjust the IFFT due to maple normalization again\n\nli stplot(map(Re,h),color=red,labels=[\"t\",\"y(t)\"],title=\"result of I FFT\");\n \n \n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" } }{PARA 13 "" 1 "" {GLPLOT2D 384 384 384 {PLOTDATA 2 "6&-%'CURVESG6#7`q 7$$\"\"\"\"\"!$!+Yiz_h!#67$$\"\"#F*$!+;^xk=!#57$$\"\"$F*$!+,)=u7$F37$$ \"\"%F*$!+1xv^VF37$$\"\"&F*$!+6/B#[&F37$$\"\"'F*$!+\"R!zskF37$$\"\"(F* $!+K!owG(F37$$\"\")F*$!+uTa+zF37$$\"\"*F*$!+\\o3%H)F37$$\"#5F*$!+*og(f %)F37$$\"#6F*$!+wcm(R)F37$$\"#7F*$!+VKD;\")F37$$\"#8F*$!+DY%=j(F37$$\" #9F*$!+UP#z'pF37$$\"#:F*$!+Vf?ahF37$$\"#;F*$!+VH]D_F37$$\"#uT?U F37$$\"#=F*$!+a+\"*zJF37$$\"#>F*$!+#=)yX@F37$$\"#?F*$!+j!p\"f6F37$$\"# @F*$!+,Ks*e#F-7$$\"#AF*$\"+(4Y]>&F-7$$\"#BF*$\"+Bp(e9\"F37$$\"#CF*$\"+ NCy&f\"F37$$\"#DF*$\"+d6x^=F37$$\"#EF*$\"+OC%R!>F37$$\"#FF*$\"+FnI]a(F3 7$$\"#XF*$!+I%GM!oF37$$\"#YF*$!+8;\"e'eF37$$\"#ZF*$!+f`taZF37$$\"#[F*$ !+2H&>]$F37$$\"#\\F*$!+ez@W@F37$$\"#]F*$!+nc!*>sF-7$$\"#^F*$\"+oc!*>sF -7$$\"#_F*$\"+ez@W@F37$$\"#`F*$\"+2H&>]$F37$$\"#aF*$\"+f`taZF37$$\"#bF *$\"+8;\"e'eF37$$\"#cF*$\"+I%GM!oF37$$\"#dF*$\"+-p%>a(F37$$\"#eF*$\"+b fti!)F37$$\"#fF*$\"+TL\"[N)F37$$\"#gF*$\"+l5@:%)F37$$\"#hF*$\"+%=_!\\# )F37$$\"#iF*$\"+=jLpyF37$$\"#jF*$\"+VF37$$\"#wF*$!+d6x^=F37$$\"#xF*$!+NCy&f\"F37$$\"#yF*$!+Bp( e9\"F37$$\"#zF*$!+(4Y]>&F-7$$\"#!)F*$\"+-Ks*e#F-7$$\"#\")F*$\"+j!p\"f6 F37$$\"##)F*$\"+#=)yX@F37$$\"#$)F*$\"+a+\"*zJF37$$\"#%)F*$\"+>uT?UF37$ $\"#&)F*$\"+VH]D_F37$$\"#')F*$\"+Vf?ahF37$$\"#()F*$\"+UP#z'pF37$$\"#)) F*$\"+DY%=j(F37$$\"#*)F*$\"+VKD;\")F37$$\"#!*F*$\"+wcm(R)F37$$\"#\"*F* $\"+*og(f%)F37$$\"##*F*$\"+\\o3%H)F37$$\"#$*F*$\"+uTa+zF37$$\"#%*F*$\" +K!owG(F37$$\"#&*F*$\"+\"R!zskF37$$\"#'*F*$\"+6/B#[&F37$$\"#(*F*$\"+1x v^VF37$$\"#)*F*$\"+,)=u7$F37$$\"#**F*$\"+;^xk=F37$$\"$+\"F*$\"+Xiz_hF- -%&TITLEG6#Q/result~of~IFFT6\"-%+AXESLABELSG6$Q\"tF\\[mQ%y(t)F\\[m-%'C OLOURG6&%$RGBG$\"*++++\"!\")$F*F*Fi[m" 1 2 0 1 10 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "2 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }