English

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

Functional Analysis 2020-08-05 v2 Classical Analysis and ODEs

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.

Keywords

Cite

@article{arxiv.1811.07795,
  title  = {Linear perturbations of the Wigner distribution and the Cohen's class},
  author = {Elena Cordero and S. Ivan Trapasso},
  journal= {arXiv preprint arXiv:1811.07795},
  year   = {2020}
}

Comments

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