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Stationary Stochastic Process



Definition: We define a stationary stochastic process $ x(n)$ , $ n=0,\pm1,\pm2,\ldots$ as a stochastic process consisting of identically distributed random variables $ x(n)$ . In particular, all statistical measures are time-invariant.

When a stochastic process is stationary, we may measure statistical features by averaging over time. Examples below include the sample mean and sample variance.


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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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