Subject: Is correlation any good for pitch perception? From: Dmitry Terez <terez(at)SOUNDMATHTECH.COM> Date: Fri, 16 Jan 2004 21:21:12 -0000 X-Mailer:Netfirms Mailing - http://www.netfirms.comDear 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