An Interplay between Gabor and Wilson Frames

Abstract EN

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.