Time frequency signal analysis: Past, present and future trends

Abstract

This chapter is written to provide both an historical review of past work and an overview of recent advances in time-frequency signal analysis (TFSA). It is aimed at complementing the texts which appeared recently in [1], [2], [3] and [4]. The chapter is organised as follows. Section 1 discusses the need for time-frequency signal analysis, as opposed to either time or frequency analysis. Section 2 traces the early theoretical foundations of TFSA, which were laid prior to 1980. Section 3 covers the many faceted developments which occurred in TFSA in the 1980's and early 1990's. It covers bilinear or energetic time-frequency distributions (TFDs). Section 4 deals with a generalisation of bilinear TFDs to multilinear Polynomial TFDs. Section 5 provides a coverage of the Wigner- Ville trispectrum, which is a particular polynomial TFD, used for analysing Gaussian random amplitude modulated processes. In Section 6, some issues related to multicomponent signals and time-varying polyspectra are addressed. Section 7 is devoted to conclusions. 1.1