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Stationarity in a Random Process implies that its statistical characteristics do not change with time . Put another way, if one were to observe a stationary random process at some time $t$ it would be impossible to distinguish the statistical characteristics at that time from those at some other time ${t}^{\prime}$ .
Choose a Random Vector of length $N$ from a Random Process:
If we are only interested in the properties of moments up to 2nd order (mean, autocorrelation, covariance, ...), which isthe case for many practical applications, a weaker form of stationarity can be useful:
$X(t)$ is defined to be Wide Sense Stationary (or Weakly Stationary) iff:
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