The Wigner-Ville Distribution and Time-Frequency Signal Analysis

Abstract

Although time-frequency analysis of signals had its origin almost fifty years ago, there has been major development of the time-frequency distributions approach in the last two decades. The basic idea of the method is to develop a joint function of time and frequency, known as a time-frequency distribution, that can describe the energy density of a signal simultaneously in both time and frequency. In principle, the time-frequency distributions characterize phenomena in a two-dimensional time-frequency plane. Basically, there are two kinds of time-frequency representations. One is the quadratic method covering the time-frequency distributions, and the other is the linear approach including the Gabor transform, the Zak transform, and the wavelet transform analysis. So, the time-frequency signal analysis deals with time-frequency representations of signals and with problems related to their definition, estimation and interpretation, and it has evolved into a widely recognized applied discipline of signal processing. From theoretical and application points of view, the Wigner-Ville distribution (WVD) or the Wigner-Ville transform (WVT) plays a major role in the time-frequency signal analysis for the following reasons. First, it provides a high-resolution representation in both time and frequency for non-stationary signals. Second, it has the special properties of satisfying the time and frequency marginals in terms of the instantaneous power in time and energy spectrum in frequency and the total energy of the signal in the time and frequency plane.