The usual approach to Gabor analysis considers the Gabor families under the aspect of frames, i.e. more or less as stable, generating families of vectors in the concrete Hilbert space L2(Rd). They are obtained by applying so-called time-frequency shifts on a give bump function (often one takes the Gauss-function) along some lattice, typically for d = 1 for lattices of the form aZ x bZ, for a,b > 0.
This group structure implies that the dual frame (i.e. the family generating the minimal norm expansions for a given signal) is again a Gabor family, starting from the so-called canonical dual atom.

According to standard literature the quality of Gabor frames is best described by the condition number of the corresonding Gabor frame operator. For example it is known that for the Gauss window the condition ab < 1 is both a necessary and sufficient condition for the frame condition, and also that the frame bounds blow up as ab tends to the critical hyperbola ab = 1. There are also other ways to look at this question, e.g. in terms of function spaces spaces, typically the so-called modulation spaces, which allow to express time-frequency concentration of a function, in particular the dual Gabor atom. On the other hand it turns out that for most windows one can find that for lattices of decent redundancy (i.e. with a fundamental domain of size not much less than 1) also the representation of Gabor multipliers has some stability (these are series of projection operators onto the atoms of the frame). Thus based on function space concepts or alternatively numerical experiments carried out using MATLAB we have come up with a so-called compound condition number for Gabor frames, which leads to Gabor frames (i.e. choices of pairs of windows and lattices) which are optimal in an objective way, but also very well suited for applications, be it in the context of function spaces or from a numerical point of view.