POLYNOMIAL WIGNER-VILLE DISTRIBUTIONS AND THEIR RELATIONSHIP TO TIME-VARYING HIGHER-ORDER SPECTRA

The Wigner-Ville distribution (WVD) has optimal energy concentration f or linear frequency modulated (FM) signals. This paper presents a gene ralization of the WVD in order to effectively process nonlinear polyno mial FM signals. A class of polynomial WVD's (PWVD's) that give optima l concentration in the time-frequency plane for FM signals with a modu lation law of arbitrary polynomial form are defined. A class of polyno mial time-frequency distributions (PTFD's) are also defined, based on the class of PWVD's. The optimal energy concentration of the PWVD enab les it to be used for estimation of the instantaneous frequency (IF) o f polynomial FM signals. Finally, a link between PWVD's and time-varyi ng higher order spectra (TVHOS) is established. Just as the expected v alue of the WVD of a nonstationary random signal is the time-varying p ower spectrum, the expected values of the PWVD's have interpretations as reduced TVHOS.