Uncertainty principles for the quadratic‐phase Fourier transforms
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 u...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2021-09, Vol.44 (13), p.10416-10431 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Shah, Firdous A. Nisar, Kottakkaran S. Lone, Waseem Z. Tantary, Azhar Y. |
| description | 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. |
| doi_str_mv | 10.1002/mma.7417 |
| format | Article |
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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. 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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.</abstract><cop>Freiburg</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/mma.7417</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0001-8461-869X</orcidid><orcidid>https://orcid.org/0000-0002-9826-9475</orcidid><orcidid>https://orcid.org/0000-0001-5769-4320</orcidid><orcidid>https://orcid.org/0000-0002-4197-2813</orcidid></addata></record> |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | concentration‐based uncertainty principle Fourier transforms Hardy's inequality Heisenberg's inequality Inequalities logarithmic and local inequalities Principles quadratic‐phase Fourier transform Signal processing uncertainty principle Uncertainty principles |
| title | Uncertainty principles for the quadratic‐phase Fourier transforms |
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