Estimation of the Mean of a Stationary Random Process by Periodic Sampling

This paper* considers the problem, commonly encountered in detection theory, of estimating the mean of a stationary random process from samples taken periodically in a closed interval (0, T). The samples are, in general, correlated and the estimator used is the average of equally weighted samples taken in the interval. Existing results are extended to give a clearer interpretation of the dependence of the variance on the number of samples. The dependence is obtained in terms of the power spectral density of the process in the form of a modified sampling theorem.