Instantaneous quantities and uncertainty concepts for signal-dependent time-frequency distributions

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Instantaneous quantities and uncertainty concepts for signal-dependent time-frequency distributions

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dc.contributor.author Jones, G
dc.contributor.author Boashash, B
dc.date.accessioned 2011-08-09T13:26:46Z
dc.date.available 2011-08-09T13:26:46Z
dc.date.issued 1991
dc.identifier.citation Proc. SPIE 1566, 167 (1991); en_US
dc.identifier.other doi:10.1117/12.49819
dc.identifier.uri http://hdl.handle.net/10576/10733
dc.description (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). A companion is the comprehensive book on Time-Frequency Signal Analysis and Processing available at: http://www.elsevier.com/locate/isbn/0080443354 en_US
dc.description.abstract This paper presents a review of some concepts associated with time-frequency distributions-- the instantaneous frequency, group delay, instantaneous bandwidth, and marginal properties-- and generalizes them in time-frequency via rotation of coordinates. This work emphasizes the need to examine time-frequency distributions in the general time-frequency plane, rather than restricting oneself to a time and/or frequency framework. This analysis leads to a generalized uncertainty principle, which has previously been introduced in radar theory. This uncertainty principle is invariant under rotation in the time-frequency plane, and should be used instead of the traditional definition of Gabor. It is desired to smooth a time-frequency distribution that is an energy density function into one that is an energy function. Most distributions are combinations of density and energy functions but the Wigner-Ville distribution is purely a density function. By using a local version of the generalized uncertainty principle, the Wigner- Ville distribution is smoothed into a signal dependent spectrogram using an iterative algorithm. It is believed that this procedure may represent, in some way an optimum removal of signal uncertainty in the time-frequency plane. en_US
dc.language.iso en en_US
dc.publisher IEEE en_US
dc.subject Instantaneous parameters en_US
dc.subject short-time Fourier Transform en_US
dc.subject time-frequency analysis en_US
dc.subject instantaneous frequency en_US
dc.subject instantaneous bandwidth en_US
dc.subject time-frequency distributions en_US
dc.subject FM signals en_US
dc.subject time delay en_US
dc.subject group-delay en_US
dc.subject rotation invariance en_US
dc.subject IF en_US
dc.subject IB en_US
dc.subject quadratic TFDs en_US
dc.subject uncertainty principle en_US
dc.subject circular kernel en_US
dc.subject localised uncertainty en_US
dc.subject signal dependent TFDs en_US
dc.subject quadratic phase en_US
dc.subject generalized uncertainty principle en_US
dc.title Instantaneous quantities and uncertainty concepts for signal-dependent time-frequency distributions en_US
dc.type Article en_US

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