A discrete time and frequency Wigner-Ville distribution: properties and implementation

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A discrete time and frequency Wigner-Ville distribution: properties and implementation

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Title: A discrete time and frequency Wigner-Ville distribution: properties and implementation
Author: O'Toole, J; Mesbah, M; Boashash, B
Abstract: Time-frequency distributions are used in the analysis and processing of nonstationary signals. The Wigner- Ville distribution (WVD) is a fundamental time-frequency distribution uniquely satisfying many desirable mathematical properties. The realisation of this distribution for hardware or software platforms requires a discrete version. Historically the majority of the work on deriving discrete versions of the WVD has focused on creating alias-free distributions, often resulting in a loss of some desirable properties. Here a new discrete time and frequency WVD will be presented for nonperiodic signals and will be examined both in terms of its properties and aliasing. In particular unitarity, an assumed property for optimum time-frequency detection and signal estimation, and invertibility, a useful property especially for time-frequency ltering, will be examined. An ef cient implementation of the distribution using standard real-valued fast Fourier transforms will also be presented.
Description: This paper proposes an alias-free discrete time and frequency Wigner-Ville distribution for non-periodic signals. (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/10576/10818
Date: 2005-12

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