Re: Gaussian vs uniform noise audibility

["Alain de Cheveigne'" <Alain.de.Cheveigne@xxxxxxxx>]

> 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