Wigner Higher Order Moment Spectra: Definition, Properties, Computation and Application to Transient Signal Analysis

The Wigner higher order moment spectra (WHOS) are defined as extensions of the Wigner-Ville distribution (WD) to higher order moment spectra domains. A general class of time-frequency higher order moment spectra is also defined in terms of arbitrary higher order moments of the signal as generalizations of the Cohen’s general class of time-frequency representations. The properties of the general class of time-frequency higher order moment spectra can be related to the properties of WHOS which are, in fact, extensions of the properties of the WD. Discrete time and frequency Wigner higher order moment spectra (DTF-WHOS) distributions are introduced for signal processing applications and are shown to be implemented with two FFT-based algorithms. One application is presented where the Wigner bispectrum (WB), which is a WHOS in the third-order moment domain, is utilized for the detection of transient signals embedded in noise. The WB is compared with the WD in terms of simulation examples and analysis of real sonar data. It is shown that better detection schemes can be derived, in low signal-to-noise ratio, when the WB is applied.