Journal
ANALYSIS AND APPLICATIONS
Volume 18, Issue 3, Pages 385-422Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219530519500052
Keywords
Time-frequency analysis; Wigner distribution; Cohen's class; modulation spaces; Wiener amalgam spaces
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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 kinds of modifications have been proposed. This contribution fits into this perspective. We introduce a family of phase-space representations of aligner type associated with invertible matrices and explore their general properties. As a main result, we provide a characterization for the Cohen's class [L. Cohen, Generalized phase-space distribution functions, J. Math. Phys. 7 (1996) 781-786; Time-frequency Analysis (Prentice Hall, New Jersey, 1995)]. 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.
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