Time varying higher order spectra

The Wigner-Ville distribution (WVD) is a second-order time-frequency representation in the sense that it is able to give ideal energy concentration for quadratic FM signals, and its expectation value is a second-order time-varying spectrum. The authors present two methods for generalizing the WVD in order to achieve the ideal energy concentration for polynomial frequency (phase) signals. The expected values of such generalized WVDs (GWVDs) are the Fourier transforms of some particular higher-order moments and/or cumulants. The ensemble averaged GWVDs therefore have interpretation as time-varying higher-order spectra