"Metaplectic Wigner Distributions and Frames"Giacchi, GianlucaMetaplectic Wigner distributions are defined as an extreme generalization of the most popular time-frequency representations by means of metaplectic operators. Moreover, they provide deeper insights into the features that a time-frequency distribution should express in order to satisfy many reasonable properties. Defining and measuring local time-frequency content and decay of signals in phase space, covariance, positivity, belonging to Cohen's class, and being generalized spectrograms are just a few of these properties. Additionally, the symplectic invariance of Gabor frames can be formulated and explained in terms of metaplectic Gabor frames, demonstrating that Gabor frames are not only invariant with respect to symplectic transformations but also satisfy a more general invariance property with respect to any invertible matrix, with the window being deformed accordingly via metaplectic operators. This talk provides an overview of my recent research with Professors E. Cordero and L. Rodino. |
| https://ps-mathematik.univie.ac.at/e/talks/strobl24_Giacchi_2024-02_Giacchi_STROBL24.tex |
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