1 December 1991 Instantaneous quantities and uncertainty concepts for signal-dependent time-frequency distributions
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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.
© (1991) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Graeme Jones, Graeme Jones, Boualem Boashash, Boualem Boashash, } "Instantaneous quantities and uncertainty concepts for signal-dependent time-frequency distributions", Proc. SPIE 1566, Advanced Signal Processing Algorithms, Architectures, and Implementations II, (1 December 1991); doi: 10.1117/12.49819; https://doi.org/10.1117/12.49819
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