Re: Gaussian vs uniform noise audibility

[Julius Smith <jos@xxxxxxxxxxxxxxxxxx>]

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