The Generalization of the Poisson Sum Formula Associated with the Linear Canonical Transform
The generalization of the classical Poisson sum formula, by replacing the ordinary Fourier transform by the canonical transformation, has been derived in the linear canonical transform sense. Firstly, a new sum formula of Chirp-periodic property has been introduced, and then the relationship between...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/102039 |
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| _version_ | 1832564219356119040 |
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| author | Jun-Fang Zhang Shou-Ping Hou |
| author_facet | Jun-Fang Zhang Shou-Ping Hou |
| author_sort | Jun-Fang Zhang |
| collection | DOAJ |
| description | The generalization of the classical Poisson sum formula, by replacing the ordinary Fourier transform by the canonical transformation, has been derived in the linear canonical transform sense. Firstly, a new sum formula of Chirp-periodic property has been introduced, and then the relationship between this new sum and the original signal is derived. Secondly, the generalization of the classical Poisson sum formula to the linear canonical transform sense has been obtained. |
| format | Article |
| id | doaj-art-b854f53970304d7e9207c67e930bf833 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b854f53970304d7e9207c67e930bf8332025-02-03T01:11:38ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/102039102039The Generalization of the Poisson Sum Formula Associated with the Linear Canonical TransformJun-Fang Zhang0Shou-Ping Hou1Department of Basic Science, Beijing University of Agriculture, Beijing 102206, ChinaDepartment of Basic Science, Beijing University of Agriculture, Beijing 102206, ChinaThe generalization of the classical Poisson sum formula, by replacing the ordinary Fourier transform by the canonical transformation, has been derived in the linear canonical transform sense. Firstly, a new sum formula of Chirp-periodic property has been introduced, and then the relationship between this new sum and the original signal is derived. Secondly, the generalization of the classical Poisson sum formula to the linear canonical transform sense has been obtained.http://dx.doi.org/10.1155/2012/102039 |
| spellingShingle | Jun-Fang Zhang Shou-Ping Hou The Generalization of the Poisson Sum Formula Associated with the Linear Canonical Transform Journal of Applied Mathematics |
| title | The Generalization of the Poisson Sum Formula Associated with the Linear Canonical Transform |
| title_full | The Generalization of the Poisson Sum Formula Associated with the Linear Canonical Transform |
| title_fullStr | The Generalization of the Poisson Sum Formula Associated with the Linear Canonical Transform |
| title_full_unstemmed | The Generalization of the Poisson Sum Formula Associated with the Linear Canonical Transform |
| title_short | The Generalization of the Poisson Sum Formula Associated with the Linear Canonical Transform |
| title_sort | generalization of the poisson sum formula associated with the linear canonical transform |
| url | http://dx.doi.org/10.1155/2012/102039 |
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