On discrete time Wilson systems (Q2228189)

Summary: In this paper, we define the discrete time Wilson frame (DTW frame) for \(l^2(\mathbb{Z})\) and discuss some properties of discrete time Wilson frames. Also, we give an interplay between DTW frames and discrete time Gabor frames. Furthermore, a necessary and a sufficient condition for the DTW frame in terms of Zak transform are given. Moreover, the frame operator for the DTW frame is obtained. Finally, we discuss dual pair of frames for discrete time Wilson systems and give a sufficient condition for their existence.