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{TEXT 213 38 "Fast Fourier Transform ( FFT) Artifacts" }}{PARA 0 "" 0 "" {TEXT 213 0 "" }}{PARA 0 "" 0 "" {TEXT 213 75 "(to refresh the plots click !!! which will re-execute th e entire worksheet)" }}{PARA 0 "" 0 "" {TEXT 213 0 "" }}{PARA 0 "" 0 " " {TEXT 213 95 "see http://mathworld.wolfram.com/FourierSeriesSquareWa ve.html for expected square wave response" }}{PARA 0 "" 0 "" {TEXT 213 0 "" }}{PARA 0 "" 0 "" {TEXT 213 98 "FFTs give a quick way to dete rmine the Fourier transform from descrete measurements. 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"`:=`(f, array(1 .. 1024)):" "-I%mrowG6#/I+modulename G6\"I,TypesettingGI(_syslibGF'6--I#moGF$6-Q\"~F'/%,mathvariantGQ'norma lF'/%&fenceGQ&falseF'/%*separatorGF4/%)stretchyGF4/%*symmetricGF4/%(la rgeopGF4/%.movablelimitsGF4/%'accentGF4/%'lspaceGQ&0.0emF'/%'rspaceGFC -I#miGF$6%Q\"fF'/%'italicGQ%trueF'/F0Q'italicF'-F,6-Q*≔F'F/F2F 5F7F9F;F=F?/FBQ,0.2777778emF'/FEFS-FG6%Q&arrayF'FJFM-I(mfencedGF$6$-F# 6%-I#mnGF$6$Q\"1F'F/-F,6-Q#..F'F/F2F5F7F9F;F=F?/FBQ,0.2222222emF'FD-Fh n6$Q%1024F'F/F/-F,6-Q\":F'F/F2F5F7F9F;F=F?FRFT-FG6%Q%vfftF'FJFMFOFUFXF co" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "for i to 1024 do `:=`(f [i], evalf(`/`(`*`(`+`(i, `-`(1))), `*`(T)))) end do:" "-I%mrowG6#/I+m odulenameG6\"I,TypesettingGI(_syslibGF'6:-I#moGF$6/Q$forF'/%%boldGQ%tr ueF'/%,mathvariantGQ%boldF'/%+fontweightGF4/%&fenceGQ&falseF'/%*separa torGF9/%)stretchyGF9/%*symmetricGF9/%(largeopGF9/%.movablelimitsGF9/%' accentGF9/%'lspaceGQ&0.0emF'/%'rspaceGFH-F,6-Q\"~F'/F3Q'normalF'F7F:F< 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