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copyright R.J. Marks II ECE 5345 Ergodic Theorems

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copyright R.J. Marks II In many cases, an ensemble of random processes cannot be obtained. If parameters of a random process can be found from a single observation of the process, the process is said to be ergodic. Mean ergodic Distribution ergodic, etc. Ergodicity

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copyright R.J. Marks II Not Mean Ergodic Example Battery Factory Ergodicity Mean Ergodic

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copyright R.J. Marks II Mean Ergodicity Time Average If X(t) is WSS, the expected value is Good so far!

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copyright R.J. Marks II Mean Ergodicity We’d also like If so, X(t) is mean ergodic!

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copyright R.J. Marks II Mean Ergodicity Onward…

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copyright R.J. Marks II Mean Ergodicity Continuing: Rectangle Function

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copyright R.J. Marks II Mean Ergodicity More:

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copyright R.J. Marks II Mean Ergodicity

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copyright R.J. Marks II Ergodicity Thus, a WSS Random Process is mean ergodic if Similar criteria for discrete time stochastic processes.

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copyright R.J. Marks II Telegraph Signal Ergodic.

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copyright R.J. Marks II Battery Factory Not ergodic.

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copyright R.J. Marks II Autocorrelation Ergodic When, for large T, can we approximate Define, for a fixed , X(t) is thus correlation ergodic when Y (t) is mean ergodic for all .

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copyright R.J. Marks II Autocorrelation Ergodic Note Establishment of correlation ergodicity thus requires fourth order moments of X(t). Better than WSS.

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