On Mar 24 13:09 robert bristow-johnson wrote: > ... > this zero-padding issue applied to overlap-adding is for "fast > convolution", using the FFT and iFFT to accomplish simple filtering with > a possibly very long FIR filter. but it has to be FIR, not IIR. > ...
I guess in every case a filter can be made IIR or FIR, dependign on the use, but using an FFT is in a way a moderate length FIR filter, and the averagings at frame or more or less equivalent "cepstrum" should somehow reflect the nature of the projection or in other cases equalizing or phase lagging you're trying to achieve. Of course pre-state-ing a IIR is less natural than zero-ing a FIR, but all is in principle possible. As I recall in phone type of processing there can be talk of a limited number of fundamentals (even just 1) and some number of harmonics, so it could be the FFT is used as part of a compression algorithm, rather than a full-bandwidth attempt at audio processing.
I found it fascinating (back in the 80s) that the common algo in science of the time had a sort of waveform "phonebook" and (and that's fascinating me) a Feedback Loop in the encoding algorithm to minimize the decoder output distortion (harmonic- and to an extend transient-).
Of course the nature and musical feel of the output of some FFT algo will depend on what type of windows you use, and how much internal data is averaged, probably a specialist subject for the serious of mind, because even slight processing of "normal" music will get you harmonic feels and such. When using a lot of parallel FFT computations, lots of overlap-averaging, and nice shaped (and scientifically well through thought) windowing functions, you can get closer to the more general "wavelet" type of transform, which should be interesting.
Of course there's only a few right ways of approaching the "perfect convolution" with repeated FFT computations.
Theo V. -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
