Time-varying polyspectra and reduced Wigner-Ville trispectrum

This paper consists of two parts. The first part reviews a class of higher-order Wigner-Ville distributions projected onto a single frequency axis. This class is referred to as polynomial Wigner-Ville distributions (PWVDs). For random processes, the expected value of PWVDs represent time-varying higher-order moment spectra. The second part defines and studies a particular member of a class of time-varying higher-order spectra based on PWVDs, namely a reduced Wigner-Ville trispectrum (RWVT). This novel time-frequency representation is shown to be a very efficient tool for analysis of FM signals affected by Gaussian amplitude modulation. In the paper, we present a statistical comparison of the RWVT and WVD based instantaneous frequency estimates for linear FM signals in absence and in presence of multiplicative noise. For multicomponent signals, the RWVT has to be re-defined and calculated in the full multi-lag domain.