Basic Concepts of Random Processes
Definitions :: Ergodicity :: Autocorrelations :: Sinusoidal :: Poisson :: Gaussian :: Properties :: Spectra :: Cases :: Random :: Independent
Means and Autocorrelations
For a second order r.p.,
and
for all
.
Properties of Autocorrelation functions
 . (This is the second moment)
 (Schwartz inequality)
 (symmetric)
Widesense stationarity
Since
depends only on
, we write (by an ``abuse of
notation'')
Thus,
If a random process is second order and strictly stationary, it must also be WSS. On the other hand, if a process is WSS, it is not necessarily strictly stationary.
We say a process is covariant stationary if depends only on , or, equivalently, depends only on .
Properties of for WSS r.p.s
 (independent of )
 .
 (even function)

A defining property of these functions:
Any function with this property is a nonnegative definite function.