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- Title
An Interplay between Gabor and Wilson Frames.
- Authors
Kaushik, S. K.; Panwar, Suman
- Abstract
Wilson frames {kj : 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.
- Subjects
GABOR transforms; FRAMES (Vector analysis); GENERALIZATION; BESSEL functions; MATHEMATICAL sequences; ZAK transform
- Publication
Journal of Function Spaces & Applications, 2013, p1
- ISSN
0972-6802
- Publication type
Article
- DOI
10.1155/2013/610917