Ergodicity in the mean depends on the asymptotic behavior, Basic Statistics

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Ergodicity in the mean depends on the asymptotic behavior

Ergodicity in the mean depends on the asymptotic behavior of the auto covariance of a process, c_x(k). The asymptotic behavior of c_x(k), however, is related to the behavior of the power spectrum P_x(e^jw) at w = 0. Show that x(n) is ergodic in the mean if and only if P_x(e^jw) is continuous at the origin, w = 0.

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Basic Statistics: Ergodicity in the mean depends on the asymptotic behavior

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