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Metaplectic Wigner distributions generalize the most popular time-frequencyrepresentations, such as the short-time Fourier transform (STFT) and$\tau$-Wigner distributions, using metaplectic operators. However, in order fora metaplectic Wigner distribution to measure local time-frequency concentrationof signals, the additional property of shift-invertibility is fundamental. Inaddition, metaplectic atoms provide different ways to model signals. Namely,signals can be written as discrete superpositions of these operators, providingoriginal ways to represent signals, with applications to machine learning,signal analysis, theory of pseudodifferential operators, to mention a few.Among all shift-invertible distributions, Wigner-decomposable metaplecticWigner distributions provide the most straightforward generalization of theSTFT. In this work, we focus on metaplectic atoms of Wigner-decomposableshift-invertible metaplectic distributions and characterize the associatedmetaplectic Gabor frames.

Metaplectic Gabor frames of Wigner-Decomposable Distributions