Parseval Relationship of Samples in the Fractional Fourier Transform Domain
This paper investigates the Parseval relationship of samples associated with the fractional Fourier transform. Firstly, the Parseval relationship for uniform samples of band-limited signal is obtained. Then, the relationship is extended to a general set of nonuniform samples of band-limited signal a...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/428142 |
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| _version_ | 1832550045807804416 |
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| author | Bing-Zhao Li Tian-Zhou Xu |
| author_facet | Bing-Zhao Li Tian-Zhou Xu |
| author_sort | Bing-Zhao Li |
| collection | DOAJ |
| description | This paper investigates the Parseval relationship of samples associated with
the fractional Fourier transform. Firstly, the Parseval relationship for uniform
samples of band-limited signal is obtained. Then, the relationship is
extended to a general set of nonuniform samples of band-limited signal associated
with the fractional Fourier transform. Finally, the two dimensional
case is investigated in detail, it is also shown that the derived results can be
regarded as the generalization of the classical ones in the Fourier domain to
the fractional Fourier transform domain. |
| format | Article |
| id | doaj-art-0be2da47f58640b19e03b318dc23cc7a |
| 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-0be2da47f58640b19e03b318dc23cc7a2025-02-03T06:07:50ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/428142428142Parseval Relationship of Samples in the Fractional Fourier Transform DomainBing-Zhao Li0Tian-Zhou Xu1School of Mathematics, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Mathematics, Beijing Institute of Technology, Beijing 100081, ChinaThis paper investigates the Parseval relationship of samples associated with the fractional Fourier transform. Firstly, the Parseval relationship for uniform samples of band-limited signal is obtained. Then, the relationship is extended to a general set of nonuniform samples of band-limited signal associated with the fractional Fourier transform. Finally, the two dimensional case is investigated in detail, it is also shown that the derived results can be regarded as the generalization of the classical ones in the Fourier domain to the fractional Fourier transform domain.http://dx.doi.org/10.1155/2012/428142 |
| spellingShingle | Bing-Zhao Li Tian-Zhou Xu Parseval Relationship of Samples in the Fractional Fourier Transform Domain Journal of Applied Mathematics |
| title | Parseval Relationship of Samples in the Fractional Fourier Transform Domain |
| title_full | Parseval Relationship of Samples in the Fractional Fourier Transform Domain |
| title_fullStr | Parseval Relationship of Samples in the Fractional Fourier Transform Domain |
| title_full_unstemmed | Parseval Relationship of Samples in the Fractional Fourier Transform Domain |
| title_short | Parseval Relationship of Samples in the Fractional Fourier Transform Domain |
| title_sort | parseval relationship of samples in the fractional fourier transform domain |
| url | http://dx.doi.org/10.1155/2012/428142 |
| work_keys_str_mv | AT bingzhaoli parsevalrelationshipofsamplesinthefractionalfouriertransformdomain AT tianzhouxu parsevalrelationshipofsamplesinthefractionalfouriertransformdomain |