Wigner bispectrum, phase product smoothing and time-varying bispectra

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Wigner bispectrum, phase product smoothing and time-varying bispectra

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Title: Wigner bispectrum, phase product smoothing and time-varying bispectra
Author: Frazer, G; Boashash, B
Abstract: 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.
Description: This paper shows that a Wigner bispectrum may be computed without the imposition of lag centering and associated interpolation by using a phase product relationship, which we re-derive from properties of the Fourier transform. For computing smoothed Wigner bispectra, or time-varying bispectra, the phase product can be included in the smoothing kernel design and so requires no additional computation. (Additional details can be found in the comprehensive book on Time-Frequency Signal Analysis and Processing (see http://www.elsevier.com/locate/isbn/0080443354). In addition, the most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: www.time-frequency.net. This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia, and then continuously updated).
URI: http://hdl.handle.net/10576/10770
Date: 1993-04

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