A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform
We provide a short and simple proof of an uncertainty principle associated with the quaternion linear canonical transform (QLCT) by considering the fundamental relationship between the QLCT and the quaternion Fourier transform (QFT). We show how this relation allows us to derive the inverse transfor...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2016/5874930 |
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| _version_ | 1832556544209715200 |
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| author | Mawardi Bahri Ryuichi Ashino |
| author_facet | Mawardi Bahri Ryuichi Ashino |
| author_sort | Mawardi Bahri |
| collection | DOAJ |
| description | We provide a short and simple proof of an uncertainty principle associated with the quaternion linear canonical transform (QLCT) by considering the fundamental relationship between the QLCT and the quaternion Fourier transform (QFT). We show how this relation allows us to derive the inverse transform and Parseval and Plancherel formulas associated with the QLCT. Some other properties of the QLCT are also studied. |
| format | Article |
| id | doaj-art-33afc0b83063401dbc18a9d3b099b416 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-33afc0b83063401dbc18a9d3b099b4162025-02-03T05:45:05ZengWileyAbstract and Applied Analysis1085-33751687-04092016-01-01201610.1155/2016/58749305874930A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical TransformMawardi Bahri0Ryuichi Ashino1Department of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaDivision of Mathematical Sciences, Osaka Kyoiku University, Osaka 582-8582, JapanWe provide a short and simple proof of an uncertainty principle associated with the quaternion linear canonical transform (QLCT) by considering the fundamental relationship between the QLCT and the quaternion Fourier transform (QFT). We show how this relation allows us to derive the inverse transform and Parseval and Plancherel formulas associated with the QLCT. Some other properties of the QLCT are also studied.http://dx.doi.org/10.1155/2016/5874930 |
| spellingShingle | Mawardi Bahri Ryuichi Ashino A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform Abstract and Applied Analysis |
| title | A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform |
| title_full | A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform |
| title_fullStr | A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform |
| title_full_unstemmed | A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform |
| title_short | A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform |
| title_sort | simplified proof of uncertainty principle for quaternion linear canonical transform |
| url | http://dx.doi.org/10.1155/2016/5874930 |
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