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Re: Is correlation any good for pitch perception?
At 10:37 19.01.2004 -0500, Ramdas Kumaresan wrote:
>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.
> I wonder why ACF and spectrum are orthogonal representations and how did
>Langner demonstrate that?
Langner demonstrated by means of physiological studies that periodotopy is
orthogonal to tonotopy within ICC.
When I summarized cepstrum, ACF, and periodicity, this was of course a
simplification. According to Wiener Chintchine theorem, ACF exactly equals
the Fourier cosine transform of power density spectrum. The real-valued
cepstrum is similar. Instead of rectification by squaring, the inner ear
performs one-way rectification.
Those who are not much interested in the nitty-gritty of mathematical
variants might just compare how a simple sinusoid and a rectangular
stimulus look and sound like:
The spectrum of the pure tone is a single frequency. Its ACF resembles a
comb. It sounds harmonical.
The spectrum of the rectangle is comb-like. Its ACF is a single
autocorrelation lag. It sounds sharp.
Do not ask for unneccessary mathematical sophistication. If we got the
essence, then the details are trivial, in principle.