Time-varying higher-order spectra, generalised Wigner-Ville distribution and the analysis of underwater acoustic data

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 phase FM signals, and its expectation value is a second order time-varying spectrum. The generalized WVD (GWVD) is defined by extension so as to achieve ideal energy concentration for higher order phase laws. In addition, by taking the expected value of the GWVD, time-varying higher-order spectra can be defined. The merit of including time-varying higher-order spectral information when analyzing underwater acoustic signals is demonstrated