I just wrote a paper about speech processing. It invents a new signal transform, the "cochlear transform," which is sort of like unifying Fourier and Laplace, plus Fast ala the FFT. It includes in the final section a proof of a "Weierstrass-like approximation theorem" which settles (basically) an open problem posed by Aho, Stieglitz, and Ullman 1975 and which I had posed to this forum as an open problem, but nobody solved it for me :( Perhaps you experts on FFTs & ilk will have useful comments re the speech part and the stuff about how many arithmetic operations are used... send comments on the paper to warren.wds AT gmail.com. Paper draft here: http://dl.dropbox.com/u/3507527/SpeechProc.html -- Warren D. Smith http://RangeVoting.org  <-- add your endorsement (by clicking "endorse" as 1st step)