A note on Gabor frames in finite dimensions

TL;DR

This paper proves the existence of Gabor frames in all finite dimensions and provides tools for their explicit construction, with applications in signal recovery, operator identification, and time-frequency analysis.

Contribution

It establishes the existence of Gabor frames in finite dimensions and offers methods for their explicit construction, advancing theoretical understanding and practical applications.

Findings

Existence of Gabor frames in all finite dimensions.

Explicit construction methods for Gabor frames.

Applications in signal recovery and operator identification.

Abstract

The purpose of this note is to present a proof of the existence of Gabor frames in general linear position in all finite dimensions. The tools developed in this note are also helpful towards an explicit construction of such a frame, which is carried out in the last section. This result has applications in signal recovery through erasure channels, operator identification, and time-frequency analysis.