Wigner bispectrum, phase product smoothing and time-varying bispectra

Time-varying higher order spectra (TVHOS) based analysis is an emerging technique for analyzing signals which are non-stationary, non-Gaussian and nonlinear. Most TVHOS are derived from the Wigner-Ville distribution (WVD), and in particular, retain the lag centering property of the WVD. When extended to third and higher orders, calculation of TVHOS can be complicated by the need for signal interpolation, imposed by the requirement for lag centering. The authors derive a phase product relationship which allows the lag centred Wigner bispectrum to be computed in a simpler way using a non-lag centered time-varying bispectrum. For smoothed Wigner bispectra, the phase product term can be included in the smoothing function and so requires no additional computation. This result is demonstrated for the second-order case, where the WVD is computed using a non-lag centered Rihaczek time-frequency distribution.<>