Metaplectic Gabor Frames and Symplectic Analysis of Time-Frequency Spaces

Elena Cordero; Gianluca Giacchi

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Metaplectic Gabor Frames and Symplectic Analysis of Time-Frequency Spaces

Elena Cordero, Gianluca Giacchi

Analysis of PDEs · Submitted 10 Apr 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Thus, these metaplectic distributions (and related frames) provide meaningful definitions of local frequencies and can be used to measure effectively the local frequency content of signals.

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.18 · mentions code or data availability 0.02.

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We introduce new frames, called \textit{metaplectic Gabor frames}, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions. Namely, we develop the theory of metaplectic atoms in a full-general setting and prove an inversion formula for metaplectic Wigner distributions on $\mathbb{R}^d$. Its discretization provides metaplectic Gabor frames. Next, we deepen the understanding of the so-called shift-invertible metaplectic Wigner distributions, showing that they can be represented, up to chirps, as rescaled short-time Fourier transforms. As an application, we derive a new characterization of modulation and Wiener amalgam spaces. Thus, these metaplectic distributions (and related frames) provide meaningful definitions of local frequencies and can be used to measure effectively the local frequency content of signals.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We introduce new frames, called \textit{metaplectic Gabor frames}, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions.	contribution 1.00	0.95	0.15	asserted 1.00
s1	Namely, we develop the theory of metaplectic atoms in a full-general setting and prove an inversion formula for metaplectic Wigner distributions on $\mathbb{R}^d$.	contribution 0.93	0.96	0.17	asserted 1.00
s2	Its discretization provides metaplectic Gabor frames.	method 0.66	0.80	0.09	asserted 1.00
s3	Next, we deepen the understanding of the so-called shift-invertible metaplectic Wigner distributions, showing that they can be represented, up to chirps, as rescaled short-time Fourier transforms.	result 0.57	0.90	0.10	asserted 1.00
s4	As an application, we derive a new characterization of modulation and Wiener amalgam spaces.	result 0.85	0.95	0.12	asserted 1.00
s5	Thus, these metaplectic distributions (and related frames) provide meaningful definitions of local frequencies and can be used to measure effectively the local frequency content of signals.	interpretation 1.00	0.74	0.58	asserted 0.91

What kind of paper the classifier reports this is: theoretical result 0.65 · evidence from proof or derivation 1.00.

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Original abstract

We introduce new frames, called \textit{metaplectic Gabor frames}, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions. Namely, we develop the theory of metaplectic atoms in a full-general setting and prove an inversion formula for metaplectic Wigner distributions on $\mathbb{R}^d$. Its discretization provides metaplectic Gabor frames. Next, we deepen the understanding of the so-called shift-invertible metaplectic Wigner distributions, showing that they can be represented, up to chirps, as rescaled short-time Fourier transforms. As an application, we derive a new characterization of modulation and Wiener amalgam spaces. Thus, these metaplectic distributions (and related frames) provide meaningful definitions of local frequencies and can be used to measure effectively the local frequency content of signals.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Their main properties were investigated in [ref] ; in particular, we recall the issues below.

Metaplectic Gabor frames of Wigner-Decomposable Distributions · Metaplectic Wigner distributions and Atoms · 0.91

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