  Metaplectic Wigner distributions generalize the most popular time-frequency
representations, such as the short-time Fourier transform (STFT) and
$\tau$-Wigner distributions, using metaplectic operators. However, in order for
a metaplectic Wigner distribution to measure local time-frequency concentration
of signals, the additional property of shift-invertibility is fundamental. In
addition, metaplectic atoms provide different ways to model signals. Namely,
signals can be written as discrete superpositions of these operators, providing
original 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 metaplectic
Wigner distributions provide the most straightforward generalization of the
STFT. In this work, we focus on metaplectic atoms of Wigner-decomposable
shift-invertible metaplectic distributions and characterize the associated
metaplectic Gabor frames.
