Chirp Signal Transform and Its Properties
The chirp signal exp(iπ(x-y)2) is a typical example of CAZAC (constant amplitude zero autocorrelation) sequence. Using the chirp signals, the chirp z transform and the chirp-Fourier transform were defined in order to calculate the discrete Fourier transform. We define a transform directly from the c...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/161989 |
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| author | Mio Horai Hideo Kobayashi Takashi G. Nitta |
| author_facet | Mio Horai Hideo Kobayashi Takashi G. Nitta |
| author_sort | Mio Horai |
| collection | DOAJ |
| description | The chirp signal exp(iπ(x-y)2) is a typical example of CAZAC (constant amplitude zero autocorrelation) sequence. Using the chirp signals, the chirp z transform and the chirp-Fourier transform were defined in order to calculate the discrete Fourier transform. We define a transform directly from the chirp signals for an even or odd number N and the continuous version. We study the fundamental properties of the transform and how it can be applied to recursion problems and differential equations. Furthermore, when N is not prime and N=ML, we define a transform skipped L and develop the theory for it. |
| format | Article |
| id | doaj-art-3b14fb3bdb4f4d4abff945d12550bf09 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-3b14fb3bdb4f4d4abff945d12550bf092025-08-20T03:55:36ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/161989161989Chirp Signal Transform and Its PropertiesMio Horai0Hideo Kobayashi1Takashi G. Nitta2Department of Electrical and Electronic Engineering, Faculty of Engineering Graduate school of Engineering, Mie University, Kurimamachiyamachi, Tsu 514-8507, JapanDepartment of Electrical and Electronic Engineering, Faculty of Engineering Graduate school of Engineering, Mie University, Kurimamachiyamachi, Tsu 514-8507, JapanDepartment of Mathematics, Faculty of Education, Mie University, Kurimamachiyamachi, Tsu 514-8507, JapanThe chirp signal exp(iπ(x-y)2) is a typical example of CAZAC (constant amplitude zero autocorrelation) sequence. Using the chirp signals, the chirp z transform and the chirp-Fourier transform were defined in order to calculate the discrete Fourier transform. We define a transform directly from the chirp signals for an even or odd number N and the continuous version. We study the fundamental properties of the transform and how it can be applied to recursion problems and differential equations. Furthermore, when N is not prime and N=ML, we define a transform skipped L and develop the theory for it.http://dx.doi.org/10.1155/2014/161989 |
| spellingShingle | Mio Horai Hideo Kobayashi Takashi G. Nitta Chirp Signal Transform and Its Properties Journal of Applied Mathematics |
| title | Chirp Signal Transform and Its Properties |
| title_full | Chirp Signal Transform and Its Properties |
| title_fullStr | Chirp Signal Transform and Its Properties |
| title_full_unstemmed | Chirp Signal Transform and Its Properties |
| title_short | Chirp Signal Transform and Its Properties |
| title_sort | chirp signal transform and its properties |
| url | http://dx.doi.org/10.1155/2014/161989 |
| work_keys_str_mv | AT miohorai chirpsignaltransformanditsproperties AT hideokobayashi chirpsignaltransformanditsproperties AT takashignitta chirpsignaltransformanditsproperties |