Realization adaptive strategies and a comparison of Fourier bandwidth, Shannon bandwidth, and Campbell bandwidth

In 1960, Campbell derived a quantity that he defined as the coefficient rate of a random process that involves the process spectral entropy. However, no potential applications of the coefficient rate were identified. Two new derivations of Campbell´s rate coefficient rate are presented. One derivation solidifies the interpretation of this quantity as a coefficient rate and allows definition of an effective bandwidth for the process. The second derivation implies a new approach for realization adaptive source compression. The coefficient rate can be used for realization adaptive coefficient selection in a sequence of source representations. Furthermore, the effective bandwidth is designated as Campbell bandwidth and contrasted with Fourier bandwidth and Shannon bandwidth. Several specific examples are presented that illustrate the differences among the three quantities.