The usefulness of Gabor frames depends on the easy computability of a suitable dual window. This question is addressed under several aspects. Several versions of Schulz's iterative algorithm for the approximation of the canonical dual window are analyzed for their numerical stability. For Gabor frames with totally positive windows or with exponential B-splines, a direct algorithm yields a family of exact dual windows with compact support. It is shown that these dual windows converge exponentially fast to the canonical dual window.

In this paper, a large class of universal windows for Gabor frames (Weyl-Heisenberg frames) is constructed. These windows have the fundamental property that every overcritical rectangular lattice generates a Gabor frame. Likewise, every undercritical rectangular lattice generates a Riesz sequence.