Abstract: An approach for characterizing the properties of basisfunctions which constitute a finite scheme of discreteGabor representation is presented in the context ofoversampling. The approach is based on the concept offrames and utilizes the Piecewise Finite Zak Transform(PFZT). The frame operator associated with theGabor-type frame is examined by representing the frameoperator as a matrix-valued function in the PFZTdomain. The frame property of the Gabor representationfunctions are examined in relation to the properties ofthe matrix-valued function. The frame bounds arecalculated by means of the eigenvalues of thematrix-valued function, and the dual frame, which isused in calculation of the expansion coefficients, isexpressed by means of the inverse matrix. DFT-basedalgorithms for computation of the expansioncoefficients, and for the reconstruction of signalsfrom these coefficients are generalized for the case ofoversampling of the Gabor space.!8
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