An Interplay between Gabor and Wilson Frames
Wilson frames {ψjk:w0,w-1∈L2(ℝ)}j∈ℤ,k∈ℕ0 as a generalization of Wilson bases have been defined and studied. We give necessary condition for a Wilson system to be a Wilson frame. Also, sufficient conditions for a Wilson system to be a Wilson Bessel sequence are obtained. Under the assumption that the...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/610917 |
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| author | S. K. Kaushik Suman Panwar |
| author_facet | S. K. Kaushik Suman Panwar |
| author_sort | S. K. Kaushik |
| collection | DOAJ |
| description | Wilson frames {ψjk:w0,w-1∈L2(ℝ)}j∈ℤ,k∈ℕ0 as a generalization of Wilson bases have been defined and studied. We give necessary condition for a Wilson system to be a Wilson frame. Also, sufficient conditions for a Wilson system to be a Wilson Bessel sequence are obtained. Under the assumption that the window functions w0 and w-1 for odd and even indices of j
are the same, we obtain sufficient conditions for a Wilson system to be a Wilson frame (Wilson Bessel sequence). Finally, under the same conditions, a characterization of Wilson frame in terms of Zak transform is given. |
| format | Article |
| id | doaj-art-eaff4a8059144a9ca5c21b9fc3c756f7 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-eaff4a8059144a9ca5c21b9fc3c756f72025-02-03T01:01:46ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/610917610917An Interplay between Gabor and Wilson FramesS. K. Kaushik0Suman Panwar1Department of Mathematics, Kirori Mal College, University of Delhi, Delhi 110 007, IndiaDepartment of Mathematics, University of Delhi, Delhi 110 007, IndiaWilson frames {ψjk:w0,w-1∈L2(ℝ)}j∈ℤ,k∈ℕ0 as a generalization of Wilson bases have been defined and studied. We give necessary condition for a Wilson system to be a Wilson frame. Also, sufficient conditions for a Wilson system to be a Wilson Bessel sequence are obtained. Under the assumption that the window functions w0 and w-1 for odd and even indices of j are the same, we obtain sufficient conditions for a Wilson system to be a Wilson frame (Wilson Bessel sequence). Finally, under the same conditions, a characterization of Wilson frame in terms of Zak transform is given.http://dx.doi.org/10.1155/2013/610917 |
| spellingShingle | S. K. Kaushik Suman Panwar An Interplay between Gabor and Wilson Frames Journal of Function Spaces and Applications |
| title | An Interplay between Gabor and Wilson Frames |
| title_full | An Interplay between Gabor and Wilson Frames |
| title_fullStr | An Interplay between Gabor and Wilson Frames |
| title_full_unstemmed | An Interplay between Gabor and Wilson Frames |
| title_short | An Interplay between Gabor and Wilson Frames |
| title_sort | interplay between gabor and wilson frames |
| url | http://dx.doi.org/10.1155/2013/610917 |
| work_keys_str_mv | AT skkaushik aninterplaybetweengaborandwilsonframes AT sumanpanwar aninterplaybetweengaborandwilsonframes AT skkaushik interplaybetweengaborandwilsonframes AT sumanpanwar interplaybetweengaborandwilsonframes |