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Uncertainty principles for the quadratic‐phase Fourier transforms
Author(s) -
Shah Firdous A.,
Nisar Kottakkaran S.,
Lone Waseem Z.,
Tantary Azhar Y.
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7417
Subject(s) - mathematics , fourier transform , uncertainty principle , fourier inversion theorem , logarithm , quadratic equation , affine transformation , fractional fourier transform , phase correlation , fourier analysis , mathematical analysis , pure mathematics , physics , quantum mechanics , quantum , geometry
The quadratic‐phase Fourier transform (QPFT) is a recent addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier transform. In this article, we formulate several classes of uncertainty principles for the QPFT. Firstly, we formulate the Heisenberg's uncertainty principle governing the simultaneous localization of a signal and the corresponding QPFT. Secondly, we obtain some logarithmic and local uncertainty inequalities such as Beckner and Sobolev inequalities for the QPFT. Thirdly, we study several concentration‐based uncertainty principles, including Nazarov's, Amrein–Berthier–Benedicks's, and Donoho–Stark's uncertainty principles. Finally, we conclude the study with the formulation of Hardy's and Beurling's uncertainty principles for the QPFT.