Stationary sequence

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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:

FX(xn,xn + 1,...,xn + N − 1;n,n + 1,...,n + N − 1) = FX(xn,xn + 1,...,xn + 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

[edit] 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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