Chapter 5 - Design of Time-Frequency Distributions

Abstract

This chapter discusses the design of time frequency distribution (TFD). One of the first TFDs constructed on this basis is the Gaussian kernel distribution, a TFD designed for its reduced interference properties. To better adapt to the signal under analysis and achieve higher resolution and concentration performance, adaptive TFDs can be designed using optimization theory. TFDs can also be designed and adapted to a specific class of signals such as polynomial frequency modulation (FM) signals, leading to the formulation of polynomial WVDS. The design of such methods can be related mathematically to the theory of polynomial derivatives, thus allowing for a revised design procedure. Another example of TFDs adapted to a particular class of signals is that of TFDs adapted to signals with dispersive group delay. Another step by step methodology for the design of a specific TFD is provided using separable kernels. In addition, the class of generalized marginal TFDs is related to the fractional Fourier transform, allowing further design possibilities.