Coefficient rate and lossy source coding

Campbell derived and defined a quantity called the coefficient rate of a random process that involves the process spectral entropy. In this correspondence, his interpretation is substantiated with two new derivations. One derivation tightens the connection to source bandwidth, while the second derivation implies a specific approach to adaptive coefficient selection in realization-adaptive approaches to compression. After a discussion on the role the coefficient rate plays in adaptive source coding, a quantity called Campbell bandwidth is defined based on its connection to source bandwidth and is contrasted with Fourier bandwidth and Shannon bandwidth. The connection between coefficient rate and reverse water-filling from rate distortion theory is also demonstrated.