The effect of sampling rate on autocorrelation estimation

In power spectral estimation of a continuous band-limited random process, one must usually estimate the continuous autocorrelation function at lags which are multiples of the Nyquist interval. This is done by sampling the random process at the Nyquist rate and basing the autocorrelation lag estimates on these samples. It is shown, however, that to approximately minimize the mean-square error of these estimates, one should sample at twice the Nyquist rate. The resultant decrease in mean-square error is most pronounced for short data records. For longer data records, the use of Nyquist rate sampling proves to be adequate.