The Interpretation of Spectral Entropy Based Upon Rate Distortion Functions

In 1960 Campbell derived a quantity that he called coefficient rate which is expressible in terms of the entropy of the process power spectral density. Later, Yang, et al showed that the spectral entropy is proportional to the logarithm of the equivalent bandwidth of the smallest frequency band containing most of the energy. Gibson, et al also showed that for discrete time AR(1) sequences, Campbell's coefficient rate and Shannon's entropy rate power are equal but that the equality does not hold for higher order AR processes. In this paper, we derive a new expression for Campbell's coefficient rate in terms of the parametrized version of the rate distortion function of a Gaussian random process with a given power spectral density subject to the MSE fidelity criterion. We also derive expressions for the entropy rate power and coefficient rate in terms of the slope of the rate distortion function for the given source and for a source with flat power spectral density