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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: Gaussian vs uniform noise audibility*From*: Julius Smith <jos@xxxxxxxxxxxxxxxxxx>*Date*: Fri, 23 Jan 2004 11:11:51 -0800*Delivery-date*: Fri Jan 23 14:45:48 2004*In-reply-to*: <200401231611.i0NGBf9B014296@staff2.cso.uiuc.edu>*References*: <200401231611.i0NGBf9B014296@staff2.cso.uiuc.edu>*Reply-to*: Julius Smith <jos@xxxxxxxxxxxxxxxxxx>*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. As a result, the Fourier transform of almost any type of stationary random process yields a set of iid complex Gaussian random variables. On a more practical level, two spectral samples from a (finite-length) FFT can be regarded as independent as long as they are separated by at least one "resolution cell" --- i.e., the "band slices" they represent do not overlap significantly. For a rectangular window, the width of a resolution cell can be defined conservatively as twice the sampling rate divided by the window length. For Hamming and Hann windows, it's double that of the rectangular window, Blackman three times, and so on. In summary, any time a noise process has been heavily filtered, it can be regarded as approximately Gaussian, by the central limit theorem, and disjoint spectral regions are statistically independent. -- Julius Reference: http://mathworld.wolfram.com/CentralLimitTheorem.html

**Follow-Ups**:**Re: Gaussian vs uniform noise audibility***From:*John Hershey

**Re: Gaussian vs uniform noise audibility***From:*Alain de Cheveigne'

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

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