Coherence in Multiple Random Processes

Abstract

A multivariate coherence function is described that gives a quantitative measure of the degree of linear dependence of a random process on a set of n other random processes. The properties of this function are discussed in relation to familiar properties of the coherence function for two random processes. This bivariate case constitutes a special case of the more general problem. The effect of transmission of signals through linear systems both with and without noise and the role of coherence in optimum multivariate linear filtering are discussed.