Is correlation any good for pitch perception?

[Dmitry Terez <terez@xxxxxxxxxxxxxxxxx>]

Dear Auditory List Members,

I would like to convey some thoughts on the much-discussed subject of
how human auditory system can use autocorrelation analysis for pitch
perception.

Are you really sure that our auditory system uses autocorrelation at
all?
Has anybody seen it really happening in the brain? As far as I
understand
(Forgive me if I am wrong), beyond the cochlea not much is really
known about the real mechanism behind an exceptionally robust human
pitch perception. I am not an auditory scientist, but it just looks
to me that the correct answer on your part is “We do not know”.

I do think that correlation function has two fatal drawbacks, as far
as pitch detection is concerned  (I am talking about a classical auto-
 or cross-correlation function of a signal, that is, a multiply-and-
add type of operation, as defined in any textbook on signal
processing)

The first fatal drawback of correlation is the abundance of secondary
peaks due to complex harmonic structure of a signal. 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).

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.

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

As some of you may know, recently we introduced a new revolutionary
concept of pitch detection. It has nothing to do with correlation
(although one can see some similarity) or spectrum of a signal. It is
basically based on “unfolding” a scalar signal in several dimensions –
 a concept of signal “embedding”, as it is called in nonlinear and
chaotic signal processing.
The ICASSP paper and the Matlab demo are available from
http://www.soundmathtech.com/pitch

You can also read our US patent application publication No.
20030088401
at http://www.uspto.gov/patft

Although a purely digital implementation is described, I can build a
simple analog electro-mechanical device (basically a mechanical part
followed by a two-dimensional grid of “neurons” for projecting an
output) that is based on the same principle and is exceptionally
robust at detecting pitch.

My question is: Can our auditory system use this type of processing
for pitch perception?

Is it possible to find some mechanism that can perform this kind of
processing, perhaps between the cochlea and the brain?

I do not expect a quick answer. Please, take your time, maybe next 10
years …

Also, I would like to add that although words like “chaos
theory”, “phase space” or “signal embedding” might seem not relevant
to your research on pitch perception, they are now, in fact. This is
an entirely new game…


Best Regards,

Dmitry E. Terez, Ph.D.

SoundMath Technologies, LLC
P.O. Box 846
Cherry Hill, New Jersey, 08003
USA
e-mail: dterez AT soundmathtech.com