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To overcome the impossibility of representing the energy of a signalsimultaneously in time and frequency, many time-frequency representations havebeen introduced in the literature. Some of these are recalled in theIntroduction. In this work we propose a unified approach of the previous theoryby means of metaplectic Wigner distributions $W_{\mathcal{A}}$, with$\mathcal{A}$ symplectic matrix in $Sp(2d,\mathbb{R})$, which were introducedby Cordero, Rodino (2022) and then widely studied in subsequent papers. Namely,the short-time Fourier transform and the most popular members of the Cohen'sclass can be represented via metaplectic Wigner distributions. In particular,we introduce $\mathcal{A}$-metaplectic spectrograms which contain the classicalones and their variations arising from the $\tau$-Wigner distributions ofBoggiatto, De Donno, and Oliaro (2010). We provide a complete characterizationof those $\mathcal{A}$-Wigner distributions which give rise to generalizedspectrograms. This characterization is related to the block decomposition ofthe symplectic matrix $\mathcal{A}$. Moreover, a characterization of the$L^p$-boundedness of both $\mathcal{A}$-Wigner distributions and relatedmetaplectic pseudodifferential operators is provided.

A Unified Approach to Time-Frequency Representations and Generalized Spectrogram