Wide-Sense Stationary Processes
June 2, 2021
Back to: Fundamentals of Signal Processing
A random process x(n) is wide-sense stationary (WSS) if:
- The mean μx = Ex(n) is constant with respect to n (“stationary in the mean”), and
- The autocorrelation Rxx(n,m) = E[x(n+m)x*(n)] is constant with respect to n (“stationary in correlation”).
Where E is the expectation operator and Ex(n) is the expected value of the sequence x(n) at sample-time n.
Traditionally, if the data sequence x(n) is assumed WSS, then Rxx(n,m) is written as Rxx(m).
- Papoulis, Anthanasios, Probability, Random Variables, and Stochastic Processes, 3rd ed. New York: McGraw-Hill, 1991.
- Greenhoe, Daniel J., A Book Concerning Digital Signal Processing. Self-published, 2019.