Time-Frequency Signal Processing: A Statistical Perspective

Time-frequency methods are capable of analyzing and/or processing nonstationary signals and systems in an intuitively appealing and physically meaningful manner. This tutorial paper presents an overview of some time-frequency methods for the analysis and processing of nonstationary random signals, with emphasis placed on time-varying power spectra and techniques for signal estimation and detection. We discuss two major definitions of time-dependent power spectra— the generalized Wigner-Ville spectrum and the generalized evolutionary spectrum—and show their approximate equivalence for underspread random processes. Time-dependent power spectra are then applied to nonstationary signal estimation and detection. Specifically, simple expressions and designs of signal estimators (Wiener filters) and signal detectors in the stationary case are extended to underspread nonstationary processes. This results in time-frequency techniques for nonstationary signal estimation and detection which are intuitively meaningful as well as efficient and stable.