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:

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

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

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