Relation between Quaternion Fourier Transform and Quaternion Wigner-Ville Distribution Associated with Linear Canonical Transform
The quaternion Wigner-Ville distribution associated with linear canonical transform (QWVD-LCT) is a nontrivial generalization of the quaternion Wigner-Ville distribution to the linear canonical transform (LCT) domain. In the present paper, we establish a fundamental relationship between the QWVD-LCT...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2017/3247364 |
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| author | Mawardi Bahri Muh. Saleh Arif Fatimah |
| author_facet | Mawardi Bahri Muh. Saleh Arif Fatimah |
| author_sort | Mawardi Bahri |
| collection | DOAJ |
| description | The quaternion Wigner-Ville distribution associated with linear canonical transform (QWVD-LCT) is a nontrivial generalization of the quaternion Wigner-Ville distribution to the linear canonical transform (LCT) domain. In the present paper, we establish a fundamental relationship between the QWVD-LCT and the quaternion Fourier transform (QFT). Based on this fact, we provide alternative proof of the well-known properties of the QWVD-LCT such as inversion formula and Moyal formula. We also discuss in detail the relationship among the QWVD-LCT and other generalized transforms. Finally, based on the basic relation between the quaternion ambiguity function associated with the linear canonical transform (QAF-LCT) and the QFT, we present some important properties of the QAF-LCT. |
| format | Article |
| id | doaj-art-e5b8c438cfc5446fb2c51154d462b068 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e5b8c438cfc5446fb2c51154d462b0682025-08-20T03:26:17ZengWileyJournal of Applied Mathematics1110-757X1687-00422017-01-01201710.1155/2017/32473643247364Relation between Quaternion Fourier Transform and Quaternion Wigner-Ville Distribution Associated with Linear Canonical TransformMawardi Bahri0Muh. Saleh Arif Fatimah1Department of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaDepartment of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaThe quaternion Wigner-Ville distribution associated with linear canonical transform (QWVD-LCT) is a nontrivial generalization of the quaternion Wigner-Ville distribution to the linear canonical transform (LCT) domain. In the present paper, we establish a fundamental relationship between the QWVD-LCT and the quaternion Fourier transform (QFT). Based on this fact, we provide alternative proof of the well-known properties of the QWVD-LCT such as inversion formula and Moyal formula. We also discuss in detail the relationship among the QWVD-LCT and other generalized transforms. Finally, based on the basic relation between the quaternion ambiguity function associated with the linear canonical transform (QAF-LCT) and the QFT, we present some important properties of the QAF-LCT.http://dx.doi.org/10.1155/2017/3247364 |
| spellingShingle | Mawardi Bahri Muh. Saleh Arif Fatimah Relation between Quaternion Fourier Transform and Quaternion Wigner-Ville Distribution Associated with Linear Canonical Transform Journal of Applied Mathematics |
| title | Relation between Quaternion Fourier Transform and Quaternion Wigner-Ville Distribution Associated with Linear Canonical Transform |
| title_full | Relation between Quaternion Fourier Transform and Quaternion Wigner-Ville Distribution Associated with Linear Canonical Transform |
| title_fullStr | Relation between Quaternion Fourier Transform and Quaternion Wigner-Ville Distribution Associated with Linear Canonical Transform |
| title_full_unstemmed | Relation between Quaternion Fourier Transform and Quaternion Wigner-Ville Distribution Associated with Linear Canonical Transform |
| title_short | Relation between Quaternion Fourier Transform and Quaternion Wigner-Ville Distribution Associated with Linear Canonical Transform |
| title_sort | relation between quaternion fourier transform and quaternion wigner ville distribution associated with linear canonical transform |
| url | http://dx.doi.org/10.1155/2017/3247364 |
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