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• W4381415895 abstract "Inspired by a definition of the closed-form instantaneous cross-correlation Wigner distribution (Zhang, 2019), we generalize the notion of Wigner distribution to the so-called free metaplectic Wigner distribution (FMWD) through three free metaplectic transforms, in order to tackle a challenge in high-dimensional complex features information processing. We provide some representative special cases for this general form, including the <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$N$ </tex-math></inline-formula> -dimensional nonseparable affine characteristic Wigner distribution, kernel function Wigner distribution, convolution representation Wigner distribution and instantaneous cross-correlation Wigner distribution. We establish the standard Heisenberg’s uncertainty principles (HUPs) of the real-valued function for the FMWD. We also establish the standard HUPs of the complex-valued function for some specific (i.e., the orthogonal, the orthonormal, the minimum eigenvalue commutative and the maximum eigenvalue commutative) FMWDs. In view of the one-dimensional case of our results, we solve a burning question regarding the limit of time-frequency superresolution triggered by the linear canonical transform free parameters." @default.
• W4381415895 created "2023-06-21" @default.
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• W4381415895 date "2023-10-01" @default.
• W4381415895 modified "2023-10-14" @default.
• W4381415895 title "Free Metaplectic Wigner Distribution: Definition and Heisenberg’s Uncertainty Principles" @default.
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• W4381415895 doi "https://doi.org/10.1109/tit.2023.3287990" @default.
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