We introduce new frames, called metaplectic Gabor frames, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions, cf. [7], [8], [5], [17], [27], [28]. 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.

我们引入了新的框架，称为metaplectic Gabor框架，作为Metaplectic Wigner分布框架中Gabor框架的自然推广，参见。[7]、[8]、[5]、[17]、[27]、[28] 。也就是说，我们在完全一般的环境中发展了变质原子理论，并证明了变质维格纳分布的反演公式${\mathbb{右}}^d$。它的离散化提供了元波伽博框架。

接下来，我们加深了对所谓的移位可逆元波维格纳分布的理解，表明它们可以表示为重新缩放的短时傅里叶变换，直至线性调频。作为一个应用，我们得出了调制和维纳汞齐空间的新特征。因此，这些元波分布（和相关框架）提供了有意义的局部频率定义，并且可用于有效地测量信号的局部频率内容。