The Generalised Spectrum and Spectral Coherence of a Harmonizable Time Series

Abstract The theory of stationary time series that underlies power spectrum analysis is well known. Less well known is the theory of harmonizable time series that gives rise to spectral analysis methods appropriate for nonstationary signals. This paper reviews the spectral theory of harmonizable time series and its use in signal analysis. It begins with a brief description of the mathematical basis for the generalized spectrum of a harmonizable time series and the related notion of spectral coherence. Methods for estimating the generalized spectrum and spectral coherence are presented, and graphical displays that convey information complementary to that provided by the conventional power spectrum are described. Simulations involving periodically modulated and transient signals and application to helicopter gearbox vibration time series data demonstrate the utility of these generalized spectral analysis methods as an adjunct to conventional power spectrum analysis.