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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
ISSN1053-587X
URIhttp://hdl.handle.net/10576/10776
URIhttp://dx.doi.org/10.1109/TSP.2009.2031287
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 http://www.ieeexplore.ieee.org/. (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).
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.
Languageen
PublisherIEEE
SubjectWigner distributions
Subjectanti-aliasing
Subjectcontinuous distribution
Subjectdiscrete Fourier transforms
Subjectdiscrete time-frequency distributions
Subjectmathematical properties
Subjectquadratic time-frequency distributions
Subjecttime-frequency analysis
Subjectanalytic signal
SubjectMBD
SubjectModified B distribution
SubjectWigner-Ville Distribution
SubjectMoyal’s formula
TitleImproved Discrete Definition of Quadratic Time-Frequency Distributions
TypeArticle


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