Maximum entropy sampling frequency for stationary gaussian signals

Abstract

In various kinds of digital signal and information systems, there are strong relations between the sampling frequency of signals and the performance or efficiency of the systems. Therefore, many reports have been made on optimization of sampling frequency for various application systems. This paper discusses the problem of determining the optimum sampling frequency for stationary Gaussian signals which does not necessarily satisfy the band-limited condition of the sampling theorem. First, a brief survey of conventional decision criteria is presented. Based on a common understanding for the amount of information of a sampled datum, a new criterion is proposed that maximizes the entropy rate per one sample. For stationary Gaussian signals, it is expressed in power spectral density functions accompanied by sampling. The criterion compensates for the following defect of the conventional auto-entropy rate by subtracting the cross-entropy rate: not only does it properly reflect loss of information due to the occurrence of spectral aliasing error, but also it estimates the spectral error to be information gain. Several properties of the criterion are obtained. As numerical examples, the last part of the paper shows methods for solving the equations for the optimum sampling frequency and their solutions for signals which have nonoscillatory or oscillatory exponential auto-correlation functions.