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Linear perturbations of the Wigner distribution and the Cohen class

Elena Cordero

Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy

E-mail Address: elena.cordero@unito.it

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and

S. Ivan Trapasso

Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129 Torino, Italy

E-mail Address: salvatore.trapasso@polito.it

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https://doi.org/10.1142/S0219530519500052Cited by:26 (Source: Crossref)

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 kinds of modifications have been proposed. This contribution 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 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.

Keywords:

AMSC: 42A38, 42B35, 46F10, 46F12, 81S30

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