Frame analysis of the discrete Gabor-scheme

The properties of the discrete Gabor scheme are considered in the context of oversampling. The approach is based on the concept of frames and utilizes the piecewise finite Zak transform (PFZT). The frame operator is represented as a matrix-valued function in the PFZT domain, and its properties are examined in relation to this function. The frame hounds are calculated by means of the eigenvalues of the matrix-valued function, and the dual frame, which is used in calculation of the expansion coefkients, is expressed by means of the inverse matrix. DFT-based algorithms for computation of the expansion coeflkients, and for the reconstruction of signals from these coefficients, are generalid for the case of oversamplii of the Gabor space. The atgorithms are implemented in an example of representation of a nonstationary signal.