Tight Weyl-Heisenberg frames in l2(Z)
Tight Weyl-Heisenberg frames in l/sup 2/(Z) are the tool for short-time Fourier analysis in discrete time. They are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory. Good resolution of short-time Fourier analysis in the joint time-frequency plane is not attainable unless some redundancy is introduced. That is the reason for considering overcomplete Weyl-Heisenberg expansions. The main result of this correspondence is a complete parameterization of finite length tight Weyl-Heisenberg frames in l/sup 2/(Z) with arbitrary rational oversampling ratios. This parameterization follows from a factorization of polyphase matrices of paraunitary modulated filter banks, which is introduced first.