Coherence and its estimation via the partitioned modified chirp-Z transform

The application of the coherence function between two wide-sense stationary random processes is considered, including methods for linear and nonlinear system analysis, measuring signal-to-noise ratio, and determining time delay. Examples of misleading results owing to improper model identification and biased estimation are presented. Estimation of coherence is studied with emphasis on how practical estimation errors such as bias can be reduced. The application of the partitioned modified chirp-Z transform (PAM-CZT) for fine frequency analysis in limited bands is considered as a vehicle for reducing certain types of bias.