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Sample Mean



Definition: The sample mean of a set of $ N$ samples from a particular realization of a stationary stochastic process $ v$ is defined as the average of those samples:

$\displaystyle \hat{\mu}_{v} \isdef {\cal E}_N\{v(0:N-1)\} \isdef \frac{1}{N}\sum_{n=0}^{N-1} v(n)$ (C.17)

For a stationary stochastic process $ v$ , the sample mean is an unbiased estimator of the mean, i.e.,

$\displaystyle E\{\hat{\mu}_{v}\} = \mu_v.$ (C.18)


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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2014-06-03 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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