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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: Is correlation any good for pitch perception?*From*: Eckard Blumschein <Eckard.Blumschein@xxxxxxxxxxxxxxxxxxxxxxxxxx>*Date*: Mon, 19 Jan 2004 17:43:07 +0100*Comments*: To: Ramdas Kumaresan <kumar@ELE.URI.EDU>*Delivery-date*: Mon Jan 19 12:27:59 2004*In-reply-to*: <400BF9D7.6000606@ele.uri.edu>*References*: <3.0.5.32.20040119094436.00bb3d98@dfnserv1.urz.uni-magdeburg.de>*Reply-to*: Eckard Blumschein <Eckard.Blumschein@xxxxxxxxxxxxxxxxxxxxxxxxxx>*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

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. Eckard

**References**:**Re: Is correlation any good for pitch perception?***From:*Eckard Blumschein

**Re: Is correlation any good for pitch perception?***From:*Ramdas Kumaresan

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