An interplay between Gabor and Wilson frames

Wilson frames { ψ j k: w 0,w - 1 l 2 () } j k 0 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 w 0 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. © 2013 s. k. kaushik and suman panwar.