Re: Is correlation any good for pitch perception?

[Eckard Blumschein <Eckard.Blumschein@xxxxxxxxxxxxxxxxxxxxxxxxxx>]

Dear Dmitry Terez,

In your 2002 pitch paper you wrote:
"In summary, the proposed method appears to overcome some serious
limitations of other short -term PDAs relying on computing correlation,
spectrum or cepstrum."
You are claiming it to be not sensitive to formant structure, as fast as
possible, and robust against noise. Isn't cepstrum also insensitive and
robust? Well, I am perhaps the first one who tries to relate pitch to a
joint autocorrelation principle similar to cepstrum but opposite to
spectrum.

>Are you really sure that our auditory system uses autocorrelation at all?

There are indeed at best scant indications for autocorrelation merely
inside brain.

>For some real signals we are dealing with every day, such as speech, the
secondary
>peaks in the correlation function due to speech formants (vocal tract
resonances)
>are sometimes about the same height as the main peaks due to signal
periodicity (pitch).

This might be reasonable. However, my gut feeling does not follow the
traditional attempt to hear a pitch via the resolved harmonics of a complex
tone. Singing "a", I tend to spontaneously attribute a single pitch while
the spectrum rather looks like a comb.

>The second fatal drawback of correlation is its pitch strength
>(salience) property for simple and complex tones. In other words, the
>main peaks in the correlation function computed for, e.g. a simple
>sine wave, are too wide. Meanwhile, I would expect a simple tone to
>cause the same or even stronger pitch sensation than a complex tone
>with the same fundamental frequency.

What reason demands frequency resolution to be as coarse as corresponding
to critical bandwidth? The answer is: In order to reach sufficient temporal
resolution (accurate autocorrelation lag), one has to have enough bandwidth.

>I think that it would be strange if evolution resulted in such a
suboptimal mechanism of perceiving
>sound periodicity.

Perhaps, the mechanism is not at all suboptimal, and perception of
periodicity was never the ultimate goal. Superiority of mammal hearing is
based on increased bandwidth enabling more accurate localization as well as
more robust grouping.

>It has nothing to do with correlation
>(although one can see some similarity) or spectrum of a signal.

Please do not equate spectrum and correlation. As Gerald Langner has shown:
Cepstrum/ACF/periodicity on the one hand and spectrum on the other hand are
two orthogonal representations of the same signal.

Sincerely,
Eckard Blumschein