Time-frequency coherence - a theoretical basis for cross spectral analysis of non-stationary signals

Abstract

This paper introduces the concept of Time-frequency Coherence (TFC) between two harmonisable random processes. The TFC is based upon the Wigner-Ville Cor evolutive) spectrum (ES) as a natural extension of the stationary power spectral density. The properties of the TFC are shown to be analogous to those possessed by the stationary coherence function. An estimation procedure for the TFC is introduced based upon Cohen's class of general Time-frequency Distributions CTFD). It is shown that within this class, there is a sub-class of TFD's, called the non-degenerate class, for which this estimation procedure is welldefined. This class is precisely the class of "smoothed" periodograms. The estimation procedure is applied to the analysis of temperature gradient microstructure signals derived by vertical profiling of a turbulent fluid body.