Fourier Transforms of Finite Chirps
<p/> <p>Chirps arise in many signal processing applications. While chirps have been extensively studied as functions over both the real line and the integers, less attention has been paid to the study of chirps over finite groups. We study the existence and properties of chirps over fini...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2006-01-01
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| Series: | EURASIP Journal on Advances in Signal Processing |
| Online Access: | http://dx.doi.org/10.1155/ASP/2006/70204 |
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doaj-834750e99a644b779c88d683029d3da92020-11-24T22:59:56ZengSpringerOpenEURASIP Journal on Advances in Signal Processing1687-61721687-61802006-01-0120061070204Fourier Transforms of Finite ChirpsFickus MatthewCasazza Peter G<p/> <p>Chirps arise in many signal processing applications. While chirps have been extensively studied as functions over both the real line and the integers, less attention has been paid to the study of chirps over finite groups. We study the existence and properties of chirps over finite cyclic groups of integers. In particular, we introduce a new definition of a finite chirp which is slightly more general than those that have been previously used. We explicitly compute the discrete Fourier transforms of these chirps, yielding results that are number-theoretic in nature. As a consequence of these results, we determine the degree to which the elements of certain finite tight frames are well distributed.</p> http://dx.doi.org/10.1155/ASP/2006/70204 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Fickus Matthew Casazza Peter G |
| spellingShingle |
Fickus Matthew Casazza Peter G Fourier Transforms of Finite Chirps EURASIP Journal on Advances in Signal Processing |
| author_facet |
Fickus Matthew Casazza Peter G |
| author_sort |
Fickus Matthew |
| title |
Fourier Transforms of Finite Chirps |
| title_short |
Fourier Transforms of Finite Chirps |
| title_full |
Fourier Transforms of Finite Chirps |
| title_fullStr |
Fourier Transforms of Finite Chirps |
| title_full_unstemmed |
Fourier Transforms of Finite Chirps |
| title_sort |
fourier transforms of finite chirps |
| publisher |
SpringerOpen |
| series |
EURASIP Journal on Advances in Signal Processing |
| issn |
1687-6172 1687-6180 |
| publishDate |
2006-01-01 |
| description |
<p/> <p>Chirps arise in many signal processing applications. While chirps have been extensively studied as functions over both the real line and the integers, less attention has been paid to the study of chirps over finite groups. We study the existence and properties of chirps over finite cyclic groups of integers. In particular, we introduce a new definition of a finite chirp which is slightly more general than those that have been previously used. We explicitly compute the discrete Fourier transforms of these chirps, yielding results that are number-theoretic in nature. As a consequence of these results, we determine the degree to which the elements of certain finite tight frames are well distributed.</p> |
| url |
http://dx.doi.org/10.1155/ASP/2006/70204 |
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AT fickusmatthew fouriertransformsoffinitechirps AT casazzapeterg fouriertransformsoffinitechirps |
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