On the computation of an averaged coherence function

The coherence function provides a measure of the statistical independence of 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 channels through which a signal passes are wide-sense stationary. However, in practical situations this assumption may not be valid and the signal may actually have passed through nonstationary phase channels. This paper demonstrates that in these situations it may be better to average the cross spectrum (used to compute the coherence function) in the polar coordinate system instead of the Cartesian coordinate system. It is demonstrated that averaging the coherence function under the Cartesian coordinate system can produce an averaged estimate that is inconsistent with the meaning of the individual coherence functions that have been averaged. However, averaging the coherence function under the polar coordinate system produces an averaged coherence function that is consistent with the meaning of the individual coherence functions that have been averaged. (C) 2001 Academic Press.