Time-frequency localization operators, originally introduced by Daubechies (1988), provide a framework for localizing signals in the phase space and have become a central tool in time-frequency analysis. In this paper we introduce and study a broad generalization of these operators, called \({\mathcal {A}}\) -localization operators, associated with a metaplectic Wigner distribution \(W_{\mathcal {A}}\) and the corresponding \({\mathcal {A}}\) -pseudodifferential calculus. We first show that the classical relation between localization operators and Weyl quantization extends to any covariant metaplectic Wigner distribution. Specifically, if \(W_{\mathcal {A}}\) satisfies the covariance property \( W_{\mathcal {A}}(\pi (z)f,\pi (z)g)=T_zW_{\mathcal {A}}(f,g), \qquad z\in \mathbb {R}^{2d}, \) then \( A_{a}^{\varphi _1,\varphi _2} = \operatorname {Op}_{\mathcal {A}}\big (a * W_{\mathcal {A}}(\varphi _2,\varphi _1)\big ), \) and conversely, this identity characterizes covariance. This result extends the recent representation formula of Bastianoni and Teofanov for \(\tau \) -operators to the full metaplectic framework. We then define the \({\mathcal {A}}\) -localization operator \(A_{a,{\mathcal {A}}}^{\varphi _1,\varphi _2}\) and investigate its analytical properties. We establish boundedness results on modulation spaces and provide sufficient conditions for Schatten-von Neumann class membership. These findings connect the structure of metaplectic representations with time-frequency localization theory, offering a unified approach to quantization and signal analysis.
