Mawardi Bahri and Samsul Ariffin Abdul Karim (2022) A variation on inequality for quaternion Fourier transform, modified convolution and correlation theorems for general quaternion linear canonical transform. Symmetry, 14. pp. 1-17.
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Abstract
The quaternion linear canonical transform is an important tool in applied mathematics and it is closely related to the quaternion Fourier transform. In this work, using a symmetric form of the two-sided quaternion Fourier transform (QFT), we first derive a variation on the Heisenberg-type uncertainty principle related to this transformation. We then consider the general two-sided quaternion linear canonical transform. It may be considered as an extension of the two-sided quaternion linear canonical transform. Based on an orthogonal plane split, we develop the convolution theorem that associated with the general two-sided quaternion linear canonical transform and then derive its correlation theorem. We finally discuss how to apply general two-sided quaternion linear canonical transform to study the generalized swept-frequency filters.
| Item Type: | Article |
|---|---|
| Keyword: | Uncertainty principle, General quaternion linear canonical transform, Convolution, Correlation, Generalized Swept-frequency filters, Fourier transform |
| Subjects: | Q Science > QA Mathematics > QA1-939 Mathematics > QA71-90 Instruments and machines > QA75.5-76.95 Electronic computers. Computer science > QA76.75-76.765 Computer software T Technology > TK Electrical engineering. Electronics Nuclear engineering > TK1-9971 Electrical engineering. Electronics. Nuclear engineering > TK7800-8360 Electronics > TK7885-7895 Computer engineering. Computer hardware |
| Department: | FACULTY > Faculty of Computing and Informatics |
| Depositing User: | SITI AZIZAH BINTI IDRIS - |
| Date Deposited: | 23 Dec 2024 11:20 |
| Last Modified: | 23 Dec 2024 11:20 |
| URI: | https://eprints.ums.edu.my/id/eprint/42373 |
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