On Uncertainty Principle for Quaternionic Linear Canonical Transform
We generalize the linear canonical transform (LCT) to quaternion-valued signals, known as the quaternionic linear canonical transform (QLCT). Using the properties of the LCT we establish an uncertainty principle for the QLCT. This uncertainty principle prescribes a lower bound on the product of the...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/725952 |
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| _version_ | 1832562258575622144 |
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| author | Kit Ian Kou Jian-Yu Ou Joao Morais |
| author_facet | Kit Ian Kou Jian-Yu Ou Joao Morais |
| author_sort | Kit Ian Kou |
| collection | DOAJ |
| description | We generalize the linear canonical transform (LCT) to quaternion-valued signals, known as the quaternionic linear canonical transform (QLCT). Using the properties of the LCT we establish an uncertainty principle for the QLCT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a 2D Gaussian signal minimizes the uncertainty. |
| format | Article |
| id | doaj-art-3b0842fd4ff54655bfe37751656f3a31 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3b0842fd4ff54655bfe37751656f3a312025-02-03T01:23:02ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/725952725952On Uncertainty Principle for Quaternionic Linear Canonical TransformKit Ian Kou0Jian-Yu Ou1Joao Morais2Department of Mathematics, Faculty of Science and Technology, University of Macau, MacauDepartment of Mathematics, Faculty of Science and Technology, University of Macau, MacauCenter for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, PortugalWe generalize the linear canonical transform (LCT) to quaternion-valued signals, known as the quaternionic linear canonical transform (QLCT). Using the properties of the LCT we establish an uncertainty principle for the QLCT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a 2D Gaussian signal minimizes the uncertainty.http://dx.doi.org/10.1155/2013/725952 |
| spellingShingle | Kit Ian Kou Jian-Yu Ou Joao Morais On Uncertainty Principle for Quaternionic Linear Canonical Transform Abstract and Applied Analysis |
| title | On Uncertainty Principle for Quaternionic Linear Canonical Transform |
| title_full | On Uncertainty Principle for Quaternionic Linear Canonical Transform |
| title_fullStr | On Uncertainty Principle for Quaternionic Linear Canonical Transform |
| title_full_unstemmed | On Uncertainty Principle for Quaternionic Linear Canonical Transform |
| title_short | On Uncertainty Principle for Quaternionic Linear Canonical Transform |
| title_sort | on uncertainty principle for quaternionic linear canonical transform |
| url | http://dx.doi.org/10.1155/2013/725952 |
| work_keys_str_mv | AT kitiankou onuncertaintyprincipleforquaternioniclinearcanonicaltransform AT jianyuou onuncertaintyprincipleforquaternioniclinearcanonicaltransform AT joaomorais onuncertaintyprincipleforquaternioniclinearcanonicaltransform |