Spectral estimation based on the Wigner-Ville representation

Abstract

Several classical techniques to estimate the component frequencies in a multicomponent signal are based on Fourier-like transformations. The frequency estimates obtained from their spectral peaks are affected by the window length and phase, thus presenting a large variance even in the absence of noise. Analytic signal based spectral estimators present no phase dependence for mono-component signals but, contrary to previous claims, they are not phase invariant for multicomponent signals, and perform worse than their real signal counterparts in high noise. The analysis of Wigner-Ville (WVD) spectra of continuous and discrete signals with time-limited windows demonstrates a better frequency concentration and less phase dependence than real or analytic signal Fourier spectra. The WVD presents accurate frequency estimates for multicomponent stationary signals, where crossterm interference is attenuated by smoothing the WVD in time (SWVD). It also has an excellent performance in the presence of noise, making it a good alternative to classical spectral estimation approaches. Furthermore, it is especially appropriate for the case of nonstationary multicomponent signals due to the good WVD temporal resolution, thus representing a superior spectral estimation technique suitable for the analysis of a variety of physical processes.