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A metaplectic perspective of the uncertainty principle in the Linear Canonical Transform domain
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Orientador(es)
Resumo(s)
We derive Heisenberg uncertainty principles for pairs of Linear Canonical Transforms of a given function, by resorting to the fact that these transforms are just metaplectic operators associated with free symplectic matrices. The results obtained synthesize and generalize previous results found in the literature, because they apply to all signals, in arbitrary dimension and any metaplectic operator (which includes Linear Canonical Transforms as particular cases). Moreover, we also obtain a generalization of the Robertson-Schrödinger uncertainty principle for Linear Canonical Transforms. We also propose a new quadratic phase-space distribution, which represents a signal along two intermediate directions in the time-frequency plane. The marginal distributions are always non-negative and permit a simple interpretation in terms of the Radon transform. We also give a geometric interpretation of this quadratic phase-space representation as a Wigner distribution obtained upon Weyl quantization on a non-standard symplectic vector space. Finally, we derive the multidimensional version of the Hardy uncertainty principle for metaplectic operators and the Paley-Wiener theorem for Linear Canonical Transforms.
Descrição
Palavras-chave
Uncertainty principles Linear canonical transforms Metaplectic operators Quantum phase-space distributions
Contexto Educativo
Citação
Dias, N. C., de Gosson, M., & Prata, J. N. (2024). A metaplectic perspective of uncertainty principles in the linear canonical transform domain. Journal of Functional Analysis, 287(4), 110494
Editora
Elsevier