Yes I know, I used to do research in signal processing. Part of that complexity is because the FFT only works on power-of-2 length (e.g. 1024) input vectors so

Yes I know, I used to do research in signal processing. Part of that complexity is because the FFT only works on power-of-2 length (e.g. 1024) input vectors so they have special tricks to work with arbitrary length data. The DFT has no such restriction. I’ve read somewhere that if you apply dynamic programming to the DFT (recursive sub problems, memoization) then you end up with the FFT. One of these days I’ll try to derive that.