Subject:Re: Cepstrum computationFrom:"Alain de Cheveigne'" <Alain.de.Cheveigne(at)IRCAM.FR>Date:Wed, 23 Jun 1999 11:23:59 +0200Hi Eric, Thanks for your follow-up. The point I tried to make was that the singularities are harmless if they have "finite weight". The cepstrum can then be defined even if the log spectrum is not (in places). I suspect this to be true in practice, as a consequence of the spectrum being derived from a portion of signal limited in time, but I don't know how to prove it... If anyone does, it would be a useful contribution. But this applies only for a continuous representation. It doesn't solve the problem for a digital representation, as you pointed out, because a sample that is unlucky enough to fall at the singularity carries "infinite" weight. The thing that troubles me, supposing the above conjecture is true, is that the problem can be avoided with a continuous representation, but not with a discrete (sampled) representation. That implies a fundamental difference between digital and continuous representations. Normally we expect the two to match if the sampling rate is sufficient. How is such a mismatch possible? What I suspect is that the condition for adequate sampling of the signal (that it be band-limited to half the sampling rate) might not necessarily guarantee adequate sampling of the log spectrum. If so, the digital cepstrum is not a well defined beast. For example, there's no guarantee that values of the digital cepstrum correspond to samples of the continuous cepstrum of the same signal. Comments, anyone? Alain -------------------------------------------------------------- Alain de Cheveigne' CNRS/IRCAM, 1 place Stravinsky, 75004, Paris. phone: +33 1 44784846, fax: 44781540, email: cheveign(at)ircam.fr http://www.ircam.fr/equipes/perception/cheveign --------------------------------------------------------------

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