465 research outputs found

    Tight Weyl-Heisenberg frames in l2(Z)

    Get PDF
    Tight Weyl–Heisenberg frames in l^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^2(Z) with arbitrary rational oversampling ratios. This parame- terization follows from a factorization of polyphase matrices of paraunitary modulated filter banks, which is introduced first

    Plancherel transform criteria for Weyl-Heisenberg frames with integer oversampling

    Full text link
    We investigate the relevance of admissibility criteria based on Plancherel measure for the characterization of tight Weyl-Heisenberg frames with integer oversampling. For this purpose we observe that functions giving rise to such Weyl-Heisenberg frames are admissible with respect to the action of suitably defined type-I discrete group G. This allows to relate the construction of Weyl-Heisenberg frames to the Plancherel measure of G, which provides an alternative proof and a new interpretation of the well-known Zak transform based criterion for tight Weyl-Heisenberg frames with integer oversampling.Comment: 13 page
    • …
    corecore