Recent advances in nonstationary signal analysis: time-varying higher-order spectra and multilinear time-frequency signal analysis

Abstract

This paper is written to provide both a historical review of past work and an overview of recent advances in time-frequency signal analysis and time-varying higher-order spectra. The paper is organized as follows: Section 1 discusses the need for time-frequency signal analysis (TFSA), as opposed to either time or frequency analysis. Section 2 covers the many faceted developments which occurred in TFSA in the 1980s and early 1990s. It covers bilinear or energetic time-frequency distributions (TFDs). Section 3 deals with a generalization of bilinear TFDs to multilinear Polynomial TFDs and their relationship to time-varying higher order spectra (TVHOS). Section 4 provides a coverage of the Wigner-Ville trispectrum, which is a particular TVHOS, used for analyzing signals affected by Gaussian multiplicative noise. Section 5 is devoted to conclusions.