On the non-separable discrete Gabor signal expansion and the Zak transform

The discrete Gabor signal expansion on a lattice that is obtained by linear combinations of two independent vectors, and its relation with the discrete Zak transform are presented. It is shown how the Zak transform can be helpful in determining Gabor's signal expansion coefficients and how it can be used in finding the dual window that corresponds to a given window for this (generally non-separable) lattice