On compactly supported dual windows of Gabor frames

TL;DR

This paper characterizes all compactly supported dual windows of Gabor frames and introduces an iterative method to approximate the canonical dual window using these compactly supported duals.

Contribution

It provides a complete characterization of compactly supported dual windows and proposes an iterative approximation procedure for the canonical dual window.

Findings

Successful characterization of all compactly supported dual windows.

Development of an iterative method for approximating the canonical dual window.

Ability to approximate the dual window using functions from modulation spaces or Schwartz space.

Abstract

The main purpose of the paper is to give a characterization of all compactly supported dual windows of a Gabor frame. As an application, we consider an iterative procedure for approximation of the canonical dual window via compactly supported dual windows on every step. In particular, the procedure allows to have approximation of the canonical dual window via dual windows from certain modulation spaces or from the Schwartz space.