Stationary sequence


Stationary sequence

A stationary sequence is a random sequence such that the joint PDF (probability density function) of the sequence is invariant over time. If some random sequence X [n] is stationary then the following will hold:

F_X(x_n, x_{n+1},...,x_{n+N-1};n,n+1,...,n+N-1) = F_X(x_n, x_{n+1},...,x_{n+N-1};n+k,n+1+k,...,n+N-1+k)

If a sequence is stationary then it is wide sense stationary.

If a sequence is stationary then it has constant mean:E(X [n] ) = u_x forall n

References

*Probability and Random Processes with Application to Signal Processing Third Addition by Henry Stark and John W. Woods Prentice-Hall 2002


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