Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principles
Abstract The windowed linear canonical transform is a natural extension of the classical windowed Fourier transform using the linear canonical transform. In the current work, we first remind the reader about the relation between the windowed linear canonical transform and windowed Fourier transform....
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02737-1 |
| _version_ | 1798034727536427008 |
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| author | Mawardi Bahri |
| author_facet | Mawardi Bahri |
| author_sort | Mawardi Bahri |
| collection | DOAJ |
| description | Abstract The windowed linear canonical transform is a natural extension of the classical windowed Fourier transform using the linear canonical transform. In the current work, we first remind the reader about the relation between the windowed linear canonical transform and windowed Fourier transform. It is shown that useful relation enables us to provide different proofs of some properties of the windowed linear canonical transform, such as the orthogonality relation, inversion theorem, and complex conjugation. Lastly, we demonstrate some new results concerning several generalizations of the uncertainty principles associated with this transformation. |
| first_indexed | 2024-04-11T20:48:16Z |
| format | Article |
| id | doaj.art-6ac0b2647389476381f9c1be0ae2df7a |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-11T20:48:16Z |
| publishDate | 2022-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-6ac0b2647389476381f9c1be0ae2df7a2022-12-22T04:03:58ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-01-012022111710.1186/s13660-021-02737-1Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principlesMawardi Bahri0Department of Mathematics, Hasanuddin UniversityAbstract The windowed linear canonical transform is a natural extension of the classical windowed Fourier transform using the linear canonical transform. In the current work, we first remind the reader about the relation between the windowed linear canonical transform and windowed Fourier transform. It is shown that useful relation enables us to provide different proofs of some properties of the windowed linear canonical transform, such as the orthogonality relation, inversion theorem, and complex conjugation. Lastly, we demonstrate some new results concerning several generalizations of the uncertainty principles associated with this transformation.https://doi.org/10.1186/s13660-021-02737-1Windowed linear canonical transformUncertainty principleOrthogonality relation |
| spellingShingle | Mawardi Bahri Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principles Journal of Inequalities and Applications Windowed linear canonical transform Uncertainty principle Orthogonality relation |
| title | Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principles |
| title_full | Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principles |
| title_fullStr | Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principles |
| title_full_unstemmed | Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principles |
| title_short | Windowed linear canonical transform: its relation to windowed Fourier transform and uncertainty principles |
| title_sort | windowed linear canonical transform its relation to windowed fourier transform and uncertainty principles |
| topic | Windowed linear canonical transform Uncertainty principle Orthogonality relation |
| url | https://doi.org/10.1186/s13660-021-02737-1 |
| work_keys_str_mv | AT mawardibahri windowedlinearcanonicaltransformitsrelationtowindowedfouriertransformanduncertaintyprinciples |