Improved Discrete Definition of Quadratic Time-Frequency Distributions

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Improved Discrete Definition of Quadratic Time-Frequency Distributions

Show simple item record O'Toole, J.M Mesbah, M Boashash, B 2012-01-15T07:02:35Z 2012-01-15T07:02:35Z 2010-02
dc.identifier.citation IEEE Transactions on Signal Processing, Volume : 58 , Issue:2 On page(s): 906 - 911 en_US
dc.identifier.issn 1053-587X
dc.identifier.other Digital Object Identifier : 10.1109/TSP.2009.2031287
dc.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
dc.description.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
dc.language.iso en en_US
dc.publisher IEEE en_US
dc.subject Wigner distributions en_US
dc.subject anti-aliasing en_US
dc.subject continuous distribution en_US
dc.subject discrete Fourier transforms en_US
dc.subject discrete time-frequency distributions en_US
dc.subject mathematical properties en_US
dc.subject quadratic time-frequency distributions en_US
dc.subject time-frequency analysis en_US
dc.subject analytic signal en_US
dc.subject MBD en_US
dc.subject Modified B distribution en_US
dc.subject Wigner-Ville Distribution en_US
dc.subject Moyal’s formula en_US
dc.title Improved Discrete Definition of Quadratic Time-Frequency Distributions en_US
dc.type Article en_US

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