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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Title: Instantaneous quantities and uncertainty concepts for signal-dependent time-frequency distributions
Author: Jones, G; Boashash, B
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.
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
URI: http://hdl.handle.net/10576/10733
Date: 1991

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