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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: Robust method of fundamental frequency estimation.*From*: "Alain de Cheveigne'" <Alain.de.Cheveigne@xxxxxx>*Date*: Tue, 27 Feb 2007 17:56:32 +0100*Comments*: To: acamacho@cise.ufl.edu*Delivery-date*: Tue Feb 27 12:37:52 2007*In-reply-to*: <3043.209.251.130.178.1172552172.squirrel@webmail.cise.ufl.edu>*List-archive*: <http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>*List-help*: <http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>, <mailto:LISTSERV@LISTS.MCGILL.CA?body=INFO AUDITORY>*List-owner*: <mailto:AUDITORY-request@LISTS.MCGILL.CA>*List-subscribe*: <mailto:AUDITORY-subscribe-request@LISTS.MCGILL.CA>*List-unsubscribe*: <mailto:AUDITORY-unsubscribe-request@LISTS.MCGILL.CA>*References*: <20070131171152.74585.qmail@web26301.mail.ukl.yahoo.com> <2a17c00a0701311310i538f446ana9c8532934e57529@mail.gmail.com> <2728.209.251.130.178.1170460061.squirrel@webmail.cise.ufl.edu> <p06230900c206338eee40@[192.168.23.150]> <3043.209.251.130.178.1172552172.squirrel@webmail.cise.ufl.edu>*Reply-to*: "Alain de Cheveigne'" <Alain.de.Cheveigne@xxxxxx>*Sender*: AUDITORY - Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

Arturo,

That may be true, but there are other good time-domain > correlation-based pitch models that can NOT be expressed in terms of thespectrum.> For example, the Meddis & Hewitt or Meddis & O'Mard models, orSlaney & Lyon models, derived from Licklider's duplex theory, which do the ACF after what the cochlea model does, which is a separation into filter channels and a half-wave rectification.

I do not agree. If you know the frequency response of the cochlea, you can predict the spectrum of its output from the spectrum of its input. The effects of half-wave-rectification and compression are more difficult to analyze, but not impossible. I remember reading a little bit about it in Anssi Klapuri?s PhD thesis.

Did you consider any such models?

I have used these models in the past, but I stopped using them. If I am not wrong, what Slaney & Lyon?s model does is to apply a summary autocorrelation to the output of a gammatone filterbank (it does some extra steps, but the main idea is that one). Since this can be shown to be equivalent to applying autocorrelation to the original signal (use Wiener?Khinchin theorem and linearity property of Fourier Transform), I have not used it anymore.

For those unfamiliar, the Wiener Khinchine theorem relates the power spectrum of a signal to its autocorrelation function. One is the Fourier transform of the other. The theorem is often invoked to claim 'equivalence' between spectral and temporal (or at least autocorrelation-based) approaches.

Best, Alain

**References**:**Robust method of fundamental frequency estimation.***From:*Roisin Loughran

**Re: Robust method of fundamental frequency estimation.***From:*Yi-Wen Liu

**Re: Robust method of fundamental frequency estimation.***From:*Arturo Camacho

**Re: Robust method of fundamental frequency estimation.***From:*Richard F. Lyon

**Re: Robust method of fundamental frequency estimation.***From:*Arturo Camacho

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