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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: Gaussian vs uniform noise audibility*From*: "Alain de Cheveigne'" <Alain.de.Cheveigne@xxxxxxxx>*Date*: Sat, 24 Jan 2004 10:33:08 +0100*Delivery-date*: Sat Jan 24 05:04:29 2004*In-reply-to*: <6.0.1.1.2.20040123104845.06701ec0@w3k.org>*References*: <200401231611.i0NGBf9B014296@staff2.cso.uiuc.edu> <6.0.1.1.2.20040123104845.06701ec0@w3k.org>*Reply-to*: "Alain de Cheveigne'" <Alain.de.Cheveigne@xxxxxxxx>*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

I am surprised nobody seems to have mentioned the central limit theorem which shows that the sum of random variables from most any distribution (including uniform) converges to a Gaussian random variable.

An interesting consequence is that perceptual differences, if any, must vanish as sampling rate increases beyond the bandwidth of the acoustic system and/or ear. Every waveform value is then the weighted sum of neighboring noise samples, and thus tends to be distributed as a Gaussian. My guess is that the greatest effect is variability of instantaneous power. The ratio of mean to standard deviation of squared samples is about 0.9 for uniform noise (distributed between -1 and 1) and about 1.4 for gaussian. Cochlear filtering would reduce the non gaussianity of BM displacement values, and additional temporal smoothing (a la Plack and Moore, jasa 1990) would attenuate power fluctuations. However there might remain enough difference in variablility of excitation across time to make the noises sound different. Uniformly distributed noise would sound smoother than Gaussian as Eli originally suggested. Alain -- Alain de Cheveigne' Ircam - CNRS, 1 place Igor Stravinsky, 75004, Paris, FRANCE. email: Alain.de.Cheveigne@ircam.fr, phone: +33 1 44 78 48 46

**References**:**Re: Gaussian vs uniform noise audibility***From:*beauchamp james w

**Re: Gaussian vs uniform noise audibility***From:*Julius Smith

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