Improved Discrete Definition of Quadratic Time-Frequency Distributions

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Author O'Toole, J.M. en_US
Author Mesbah, M. en_US
Author Boashash, B. en_US
Available date 2012-01-15T07:02:35Z en_US
Publication Date 2010-02 en_US
Publication Name IEEE Transactions on Signal Processing
Citation O'Toole, J.M.; Mesbah, M.; Boashash, B., "Improved Discrete Definition of Quadratic Time-Frequency Distributions," Signal Processing, IEEE Transactions on , vol.58, no.2, pp.906,911, Feb. 2010 en_US
ISSN 1053-587X en_US
Description This paper proposes a Discrete TFD definition that satisfies all desirable properties and is (approximately) equal to samples of the continuous WVD convolved with a time-frequency kernel. Also, the proposed definition—unlike others—contains a DWVD definition that satisfies important DWVD properties such as Moyal’s formula and signal recovery. The proposed definition can be computed by simple and efficient algorithms. Matlab and Octave code to accompany this paper is available to download at (Additional details can be found in the comprehensive book on Time-Frequency Signal Analysis and Processing (see 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: 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). en_US
Abstract Computation of a time-frequency distribution (TFD) requires a discrete version of the continuous distribution. This discrete TFD (DTFD) should be free from aliasing and conserve all the important mathematical properties of the continuous distribution. Existing DTFD definitions, however, poorly approximate this ideal. One popular definition, the generalized DTFD (GDTFD), is alias free but does not retain all the desirable properties from the continuous distribution. Another definition, the so-called alias-free GDTFD (AF-GDTFD), retains most properties yet is not always alias free. We propose a new DTFD definition, based on the GDTFD, that retains all desirable properties and is always alias free. en_US
Language en en_US
Publisher IEEE en_US
Subject Wigner distributions en_US
Subject anti-aliasing en_US
Subject continuous distribution en_US
Subject discrete Fourier transforms en_US
Subject discrete time-frequency distributions en_US
Subject mathematical properties en_US
Subject quadratic time-frequency distributions en_US
Subject time-frequency analysis en_US
Subject analytic signal en_US
Subject MBD en_US
Subject Modified B distribution en_US
Subject Wigner-Ville Distribution en_US
Subject Moyal’s formula en_US
Title Improved Discrete Definition of Quadratic Time-Frequency Distributions en_US
Type Article en_US

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