From: Ron Hardin <rhhardin@mindspring.com>
Subject: Re: Karhunen Lòeve Transform
Date: Sat, 23 Jun 2001 15:28:03 GMT
Newsgroups: sci.math

Take the eigenvalues as a spectrum.  Choose _independent_
complex gaussian random variables, with variance equal to the eigenvalue,
multiply by the eigenfunction and add them up.  That gives a realization
of the process (that is, it will be Gaussian with the input correlation
function).

In the case of a stationary correlation function, Karhunen Lòeve
rediscovers the trig functions, and the eigenvalues are the ordinary
power spectrum.

Karhunen Lòeve generalizes stationary Gaussian random processes
to nonstationary ones.

You can expand a nonstationary Gaussian random process in trig functions,
but the coefficients will not be independent.
-- 
Ron Hardin
rhhardin@mindspring.com

On the internet, nobody knows you're a jerk.