Discrete Gabor transform

A feasible algorithm for implementing the Gabor expansion, the coefficients of which are computed by the discrete Gabor transform (DGT), is presented. For a given synthesis window and sampling pattern, computing the auxiliary biorthogonal function of the DGT is nothing more than solving a linear system. The DGT presented applies for both finite as well as infinite sequences. By exploiting the nonuniqueness of the auxiliary biorthogonal function at oversampling an orthogonal like DGT is obtained. As the discrete Fourier transform (DFT) is a discrete realization of the continuous-time Fourier transform, similarly, the DGT introduced provides a feasible vehicle to implement the useful Gabor expansion.>