Nonstationary Gabor Frames - Existence and Construction

TL;DR

This paper establishes the existence and construction methods for nonstationary Gabor frames, which adapt classical Gabor frames for improved signal analysis, supported by theoretical results and practical examples.

Contribution

It provides a general existence theorem, a perturbation result, and a construction approach for nonstationary Gabor frames with non-compact windows.

Findings

Existence of nonstationary Gabor frames proven.

Perturbation stability of these frames demonstrated.

Constructed frames applicable to practical signal analysis scenarios.

Abstract

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.