I really enjoyed seeing a practical use and explanation of FFTs. I learned about them in school and always hear about how great they are for audio processing, but this example finally helped me grasp their use in context. Thanks!
Great tutorial! I think I have spotted a little mistake. If one has FFT size of 512 samples and sample rate of 44kHz then in the frequency domain there are only 256 bands (complex samples) that go up to 22kHz (the half of the sampling frequency aka Nyquist frequency) and not 512 bands up to 44kHz as it is said in the video. One can confirm the band count by putting the minmax~ on the index outlet of fftin~.
I'm quite sure the pfft~ object calculates 512 bands internally (which result from the FFT) but is hiding the mirrored bands 256- 511 from you since they don't provide any additional information for the processsing. They're probably put back to your signal before the IFFT.
I know this is a broad question, but what exactly is the scope of capabilities in spectral processing? I understand the basis of how FFT works, and I've seen the examples (vocoder, cross-synthesis, spectral equalization and gating), but are there any more... musical applications for it beyond that? (I realize those are perfectly legitimate applications, but I was wondering how else it fits in for other purposes.)
there's hundreds if not probably thousands of applications for spectral processing, including noise reduction, watermarking, audio compression, all sorts of analysis including separating pitched from unpitched material, tagging/categorization of music, high-level audio scene analysis, transposition, all sorts of hybrid synthesis techniques, the list goes on.
here's a pdf to get an idea of some interesting creative techniques in analysis-resynthesis, just to get you started: