  Nonstationary Gabor frames were recently introduced in adaptive signal
analysis. They represent a natural generalization of classical Gabor frames by
allowing for adaptivity of windows and lattice in either time or frequency. In
this paper we show a general existence result for this family of frames. We
then give a perturbation result for nonstationary Gabor frames and construct
nonstationary Gabor frames with non-compactly supported windows from a related
painless nonorthogonal expansion. Finally, the theoretical results are
illustrated by two examples of practical relevance.
