On Weyl Heisenberg Frames and Balian-Low Theorem in l2(Z).

Autor: Poonam Mantry .
(Joint work with Khole Timothy Poumai and Shiv K. Kaushik) Abstract. We study the discrete time Weyl Heisenberg (DTWH) system for oversampling and critical sampling. We describe frame operator of DTWH frames as the composition of sampling operator and interpolation operator. Using discrete time Zak transform (DTZT), we characterize the dual of DTWH frames, DTWH frames and tight DTWH frames based on oversampling schemes. Also, various sampling results of DTWH systems for critical sampling are obtained. Finally, we give Balian-Low theorem of an orthonormal basis of translates and orthonormal basis formed by DTWH systems and weak Balian-Low theorem for exact DTWH frames in sequence space l2(Z).