Re: voiced/unvoiced detection

["Beerends, J.G." <J.G.Beerends@xxxxxxxxxxxxxxxx>]

In comment of the discussion below the following.
One can calculate the probability density function for the pitch from the
probability density functions of all the individual partials by creating a
stochastic subharmonic representation and applying a renormalization over
the subharmonic representations.
The exact mathematical formulation is given in the last chapter of my PhD. A
similar, more practical algorithmic, approach was given in a set of papers
(JASA) by Dik Hermes. A copy of my PhD is available for those who are
interested.

An algorithmic description can also be found in the following Philips patent
applications:
8900520 The Netherlands, 9020044007 Europe, 487462 USA, 45984/90 Japan,
Philips International B.V., Eindhoven, The Netherlands.

John Beerends
KPN Research



> ----------
> From:         Pierre Divenyi[SMTP:pdivenyi@MARVA4.NCSC.MED.VA.GOV]
> Sent:         dinsdag 10 november 1998 22:37
> To:   AUDITORY@LISTS.MCGILL.CA
> Subject:      Re: voiced/unvoiced detection
>
> At 10:11 AM 11/5/98 -0500, Keith D. Martin wrote:
>
> >....  I subscribe to the interpretation that it is the
> >alignment of these peaks across multiple channels that generates a pitch
> >sensation rather than the "sharpness" of the peaks, either in individual
> >channels or in the summary. This alignment is, of course, reflected in
> the
> >summary autocorrelation, but summing across channels is only one of many
> >ways of detecting it (this fact is pointed out in some of the papers from
> >around 1990). And the width of the peak in the summary autocorrelation
> >depends more on the strength of the various partials in a harmonic signal
> >than it does on the "pitchiness" of the sound. So the degree of
> >"pitchiness" might be related to the degree of across-channel structure
> in
> >the image....
>
> Just for the fun of making a historical argument, I would like to point
> out
> that a similar idea was expressed in 1977 by Egbert de Boer ("Pitch
> theories unified" in Psychophysics and Physiology of Hearing, E.F.Evans &
> J.P. Wilson, eds., AP, London, pp.323-334). However, de Boer did not base
> his model on autocorrelation. Rather, he obtained his pitch function
> ("cardinal function") by considering pitch formation to be a stochastic
> process in which various alternative (instantaneous) pitches may coexist.
> The width of the pitch peak, therefore, is synonymous with variability,
> i.e., the function could be regarded as a density. Of course, pitch
> uncertainty, i.e., pitch density, could look very similar to
> autocorrelations, summed or not. I can't help having a personal preference
> for the probability density interpretation because it is broad enough to
> include summary autocorrelation as well as many other models.
>
> The nicety of this model is that the problem of whispered or noisy speech
> finds an instantaneous solution. The vocal tract may be excited by any
> good
> old excitation waveform, Gussian-like noise from the bronchi, an
> artificial
> larynx vibrator, or the vocal folds in various stages of laryngitis,
> producing a continuum of standard deviation magnitudes. Naturally, the
> shape of the vocal tract does not care what the excitation waveform is
> and,
> provided the excitation is sufficiently intense, the result will be always
> the speech sound corresponding to the shape. That is, if I were able to
> whisper louder than the highway noise, I could be perfectly intelligible
> speaking in a car with the windows down, despite the fact that the
> autocorrelation of the speech I am producing would be absolutely flat.
>
> To continue history, in 1978 de Boer also wrote a more detailed version of
> the above cited paper, called "Analytic pitch theories" which he never
> published. Interested colleagues are encouraged to write him and request a
> copy. He will be very surprised...
>
>         Pierre
>
>
>
> **************************************************************************
> **
> Pierre Divenyi             Experimental Audiology Research (151)
>                                      V.A. Medical Center, Martinez, CA
> 94553, USA
> Phone: (925) 370-6745
> Fax:     (925) 228-5738
> E-mail :                       pdivenyi@marva4.ebire.org
> **************************************************************************
> **
>
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