Linear perturbations of the Wigner distribution and the Cohen's class

Abstract

The Wigner distribution is a milestone of Time-frequency Analysis. In order to cope with its drawbacks while preserving the desirable features that made it so popular, several kind of modifications have been proposed. This contributions fits into this perspective. We introduce a family of phase-space representations of Wigner type associated with invertible matrices and explore their general properties. As main result, we provide a characterization for the Cohen's class. This feature suggests to interpret this family of representations as linear perturbations of the Wigner distribution. We show which of its properties survive under linear perturbations and which ones are truly distinctive of its central role.

37 pages, 1 figure. To appear in Analysis and Applications

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• On the reduction of the interferences in the Born-Jordan distribution
• Sharp integral bounds for Wigner distributions
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• Norm Estimates for $\tau$-Pseudodifferential Operators in Wiener Amalgam and Modulation Spaces
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Cited by in corpus (4)

• Linear perturbations of the Wigner transform and the Weyl quantization
• Symplectic Analysis of Time-Frequency Spaces
• A metaplectic perspective of uncertainty principles in the Linear Canonical Transform domain
• A note on the HRT conjecture and a new uncertainty principle for the short-time Fourier transform