On the computation of an averaged coherence function

The coherence function provides a measure of the statistical independence o f two stochastic processes and is computed by using the cross spectrum and auto spectra of those processes. This paper examines the computation of an averaged coherence function from multiple blocks of data obtained from two sensors. In signal detection theory, it is generally assumed that the chann els through which a signal passes are wide-sense stationary. However, in pr actical situations this assumption may not be valid and the signal may actu ally have passed through nonstationary phase channels. This paper demonstra tes that in these situations it may be better to average the cross spectrum (used to compute the coherence function) in the polar coordinate system in stead of the Cartesian coordinate system. It is demonstrated that averaging the coherence function under the Cartesian coordinate system can produce a n averaged estimate that is inconsistent with the meaning of the individual coherence functions that have been averaged. However, averaging the cohere nce function under the polar coordinate system produces an averaged coheren ce function that is consistent with the meaning of the individual coherence functions that have been averaged. (C) 2001 Academic Press.