Such a process is said to be wide-sense stationary and is fully
defined by its *power spectrum*
representation.
The power spectrum is defined by the Fourier transform pair
with the ACF (Wiener-Kinchine theorem)

A stationary Gaussian process is thus defined by either the power spectrum or the ACF. Since the power spectrum is the Fourier transform of the autocorrelation function (ACF) with integration taken over all time, the existence of the power spectrum means that the ACF must die down to zero. This, of course, assumes there are no sinusiodal components which result in Dirac delta functions in the power spectrum.

Baggenstoss 2017-05-19