# Stationary sequence

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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:

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

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

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

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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