  The Discrete Gabor Transform (DGT) is the most commonly used transform for
signal analysis and synthesis using a linear frequency scale. It turns out that
the involved operators are rich in structure if one samples the discrete phase
space on a subgroup. Most of the literature focuses on separable subgroups, in
this paper we will survey existing methods for a generalization to arbitrary
groups, as well as present an improvement on existing methods. Comparisons are
made with respect to the computational complexity, and the running time of
optimized implementations in the C programming language. The new algorithms
have the lowest known computational complexity for nonseparable lattices and
the implementations are freely available for download. By summarizing general
background information on the state of the art, this article can also be seen
as a research survey, sharing with the readers experience in the numerical work
in Gabor analysis.
