An Interplay between Gabor and Wilson Frames - S. K. Kaushik; Suman Panwar (Journal of Function Spaces and Applications)
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.