Nonstationary Gabor frames - Existence and construction

Nonstationary Gabor frames were recently introduced in [2] and 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 also construct nonstationary Gabor frames with non-compactly supported windows from a related painless nonorthogonal expansion and give a perturbation result. Finally, the theoretical results are illustrated by two examples of practical relevance.