Discrete Subspace Multiwindow Gabor Frames and Their Duals
This paper addresses discrete subspace multiwindow Gabor analysis. Such a scenario can model many practical signals and has potential applications in signal processing. In this paper, using a suitable Zak transform matrix we characterize discrete subspace mixed multi-window Gabor frames (Riesz bases...
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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/10.1155/2013/357242 |
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| _version_ | 1832562474923065344 |
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| author | Yun-Zhang Li Yan Zhang |
| author_facet | Yun-Zhang Li Yan Zhang |
| author_sort | Yun-Zhang Li |
| collection | DOAJ |
| description | This paper addresses discrete subspace multiwindow Gabor analysis. Such a scenario can model many practical signals and has potential applications in signal processing. In this paper, using a suitable Zak transform matrix we characterize discrete subspace mixed multi-window Gabor frames (Riesz bases and orthonormal bases) and their duals with Gabor structure. From this characterization, we can easily obtain frames by designing Zak transform matrices. In particular, for usual multi-window Gabor frames (i.e., all windows have the same time-frequency shifts), we characterize the uniqueness of Gabor dual of type I (type II) and also give a class of examples of Gabor frames and an explicit expression of their Gabor duals of type I (type II). |
| format | Article |
| id | doaj-art-7295715a91af4f248dba3d35d023e7b0 |
| 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-7295715a91af4f248dba3d35d023e7b02025-02-03T01:22:34ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/357242357242Discrete Subspace Multiwindow Gabor Frames and Their DualsYun-Zhang Li0Yan Zhang1College of Applied Sciences, Beijing University of Technology, Beijing 100124, ChinaCollege of Applied Sciences, Beijing University of Technology, Beijing 100124, ChinaThis paper addresses discrete subspace multiwindow Gabor analysis. Such a scenario can model many practical signals and has potential applications in signal processing. In this paper, using a suitable Zak transform matrix we characterize discrete subspace mixed multi-window Gabor frames (Riesz bases and orthonormal bases) and their duals with Gabor structure. From this characterization, we can easily obtain frames by designing Zak transform matrices. In particular, for usual multi-window Gabor frames (i.e., all windows have the same time-frequency shifts), we characterize the uniqueness of Gabor dual of type I (type II) and also give a class of examples of Gabor frames and an explicit expression of their Gabor duals of type I (type II).http://dx.doi.org/10.1155/2013/357242 |
| spellingShingle | Yun-Zhang Li Yan Zhang Discrete Subspace Multiwindow Gabor Frames and Their Duals Abstract and Applied Analysis |
| title | Discrete Subspace Multiwindow Gabor Frames and Their Duals |
| title_full | Discrete Subspace Multiwindow Gabor Frames and Their Duals |
| title_fullStr | Discrete Subspace Multiwindow Gabor Frames and Their Duals |
| title_full_unstemmed | Discrete Subspace Multiwindow Gabor Frames and Their Duals |
| title_short | Discrete Subspace Multiwindow Gabor Frames and Their Duals |
| title_sort | discrete subspace multiwindow gabor frames and their duals |
| url | http://dx.doi.org/10.1155/2013/357242 |
| work_keys_str_mv | AT yunzhangli discretesubspacemultiwindowgaborframesandtheirduals AT yanzhang discretesubspacemultiwindowgaborframesandtheirduals |