A general class of estimators for the wigner-ville spectrum of non-stationary processes

Abstract

The Wigner-Ville spectrum is known to be the unique generalized spectrum for the time-varying spectral analysis of harmonizable processes. This time-frequency representation of a process is based on the covariance function and, for quasi-stationary processes, estimators can be defined by means of local time-averaging. We propose here a general class of such estimators relying on an arbitrary weighting function and discuss their first and second order properties in an unifying way. When specifying the arbitrary function, conventional estimators such as short-time periodograms and pseudo-Wigner estimators are recovered and can be compared. This generalized framework emphasizes the versatility of smoothed pseudo-Wigner estimators, especially for uncoupled time and frequency behaviors : they overcome the uncertainty relations of short-time periodograms which only can improve the performances in one direction of the time-frequency plane at the expense of a loss in the other one.