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AuthorO'Toole, J.M.
AuthorMesbah, M.
AuthorBoashash, B.
Available date2012-01-15T07:02:35Z
Publication Date2010-02
Publication NameIEEE Transactions on Signal Processing
CitationO'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
DescriptionThis 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).
AbstractComputation 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.
SubjectWigner distributions
continuous distribution
discrete Fourier transforms
discrete time-frequency distributions
mathematical properties
quadratic time-frequency distributions
time-frequency analysis
analytic signal
Modified B distribution
Wigner-Ville Distribution
Moyal’s formula
TitleImproved Discrete Definition of Quadratic Time-Frequency Distributions

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