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Re: Gaussian vs uniform noise audibility

I think you need the assumption that the time samples are independent and
identically distributed -- so for instance, sorting them by value would
break this assumption whereas randomly permuting them would uphold it.

If you make that assumption, then you have an i.i.d. random vector,  that
has a diagonal covariance matrix, you multiply it by a unitary matrix (such
as the Fourier transform), and look at the covariance matrix.   It is easy
to show that it is also diagonal, so there are no correlations between
frequency components either.

This only depends on the covariance in the time domain being diagonal, so it
must be true for non-Gaussian signals as well as Gaussian ones.  In fact it
is also true even if the time samples have higher-order statistical
dependencies. Conversely, higher-order statistical dependencies between the
frequencies will in general be introduced by the Fourier transform for
non-Gaussian i.i.d. distributions.  It is easy to imagine these being


----- Original Message -----
From: "Paris Smaragdis" <paris@MEDIA.MIT.EDU>
Sent: Wednesday, January 21, 2004 3:48 PM
Subject: Re: Gaussian vs uniform noise audibility

> >        Amplitude distributions in time are related to correlations
> > across
> > frequency. In gaussian noise, the amplitudes and phases of the
> > different
> > frequency components are independent. In non-gaussian noise, even with
> > white power spectrum, amplitudes and/or phases are correlated.
> Do you have a reference for these statements?  My understanding is that
> the amplitude distribution is largely irrelevant to the frequency
> content (for example if you take any signal and sort or permute it in
> time it sounds completely different yet retains the original amplitude
> distribution).
> Thanks,
> Paris