Implementations of non-separable Gabor schemes

In this paper we consider non-separable Gabor schemes for discrete-time signals. We show that three different interpretations of a non-separable lattice lead to three different types of implementation. First, interpreting the non-separable lattice as a sub-lattice of a denser rectangular lattice allows us to use the Zak transformation. Secondly, a non-separable lattice can be seen as a union of rectangular lattices, which leads to a filter bank implementation. And finally, a rectangular lattice can be obtained by shearing a non-separable lattice. As a direct consequence, conventional algorithms developed for rectangular lattices can be re-used for the non-separable case.