The discrete Gabor transform and the discrete Zak transform on a quincunx lattice

The discrete Gabor expansion on a quincunx lattice and its relation with the discrete Zak transform is 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 functions that correspond to a given elementary signal for this quincunx lattice. Furthermore, some examples are given and compared with Gabor´s signal expansion on a rectangular lattice