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.