[CST-2] Information Theory

[Matthew Richards]

> Guassian is self-Fourier, but then Dr. Daugman also said that the power
> spectrum  of gaussian is uniform (white noise)??

I was stuck by this for some time, but I think I worked out roughly the
right answer in the end.  White noise is the signal with a Gaussian
*distribution* - it's a signal which wiggles around a lot, and the
probability p(x) of being x away from the mean amplitude is given by a
Gaussian probability density function.  So the signal itself doesn't look
Gaussian, just its distribution.

If you do F(x)F*(x) on the wiggles (or convolve f with f* and take the FT),
the result you get is a flat line in the frequency domain - that's the power
spectrum, and as Dr Daugman said it's uniform and hence has maximum entropy
for given power.


Hope this helps,
Matthew