Basic Concepts of Random Processes
Definitions :: Ergodicity :: Autocorrelations :: Sinusoidal :: Poisson :: Gaussian :: Properties :: Spectra :: Cases :: Random :: Independent
Cases when does not have a transform
We examine this and other cases that are WSS but do not have a Fourier
transform (in the conventional sense).

Suppose
. Then
is continuous and is the
autocorrelation function of a WSS r.p. if and only if there is a
c.d.f.
satisfying
such that

Suppose
. Then
is the autocorrelation
function of a WSS r.p. if and only if there exists a
satisfying
such that
If
exists, then
In this case, is, in fact, a p.d.f.
More generally,
is a spectral distribution of
.