I comment on http://www.jsoftware.com/jwiki/Essays/FFT. FFT means Fast Fourier Transform and IFFT is the Inverse Fast Fourier Transform.
ifft fft i.16 0 1j_2.22045e_16 2 3j2.22045e_16 4 5j_2.22045e_16 6 7j2.22045e_16 8 9j2.22045e_16 10 11j_2.22045e_16 12 13j2.22045e_16 14 15j_2.22045e_16 1. The Cliff Reiter rounding (**|)&.+. removes the ugly deviations from exact zero. (**|)&.+. ifft fft i.16 NB. test 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 So the verb 'roundimag' from jwiki/Essays/FFT is unnecessary. 2. jwiki/Essays/FFT defines two versions of the verb 'roots', but none of them are used later. 3. In jwiki/Essays/FFT the 'root of unity' verb rou is complicated for reasons which I don't quite understand. It only works if the argument is divisible by 8. It may be defined using a 'Power of Unity' verb. The simple definitionPoU=:13 : '1^y' always produces 1 for real arguments, but'_1^+:y' works. So does '^0j2p1*y' and 'r.2p1*y', but I prefer'_1^+:y'. 4. Rather than complex conjugation of rou in the ifft verb you may conjugate the input, both in fft and ifft. 5. The division by '#' can be put inside rconvolve. Then fft and ifft becomes the same. Then the program becomes: convolve =: +//.@:(*/) NB. slow convolution extend =: >.&.(2&^.)@<:@+&#{."_1,: NB. join and extend with zeros rd =: (**|)&.+. NB. Cliff Reiter rounding PoU =: _1^+: NB. Power of Unity rou =: 13 :'PoU(i.y%2)%y' NB. roots of unity floop =: 4 :'for_r. i.#$x do. (y=.{."1 y) ] x=.(+/x) ,&,:"r (-/x)*y end.' cube =: ($~ q:@#) :. , fft =: (+floop&.cube rou@#) f. :. fft rconvolve =: [:rd(%#)@:*&.fft/@extend NB. fast convolution 1 2 3 4 convolve 2 3 4 5 NB. test 2 7 16 30 34 31 20 1 2 3 4 rconvolve 2 3 4 5 NB. test 2 7 16 30 34 31 20 0 - Bo ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm