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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0972-6802 1758-4965 |