THE WIGNER DISTRIBUTION - A TIME-FREQUENCY ANALYSIS TOOL

Time-frequency distributions are enormously powerful tools for analysi s of time series data. Often our data contain signals whose frequency content may be changing with time. Capturing this change with good fre quency and time resolutions has been the subject of much research in t he last two decades. The Wigner distribution and the associated Cohen class of generalized Wigner distributions offer a possible way to cond uct such analysis. In this article I review some of the basic features of the Wigner distribution and emphasize its relationship to the two- dimensional ambiguity function. I discuss the interference terms that arise in the Wigner distribution of multicomponent signals and define the two most popular classes of kernal functions designed to eliminate cross-term interference. I point out that experimental kernel functio ns must be designed in the Doppler-lag domain with a complete knowledg e of the signals of interest and give an example of an unusual kernel in one application. I apply the methods outlined to two real data sets obtained by APL staff during different experiments. For both sets, th e Wigner distribution with appropriate kernel functions is shown to be superior to the standard spectrogram.