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arXiv · 1710.08280

Gabor frames in $\ell^2(\mathbf Z)$ and linear dependence

Ole Christensen·Marzieh Hasannasab
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Abstract

We prove that an overcomplete Gabor frame in $ \ell^2(\mathbf Z)$ by a finitely supported sequence is always linearly dependent. This is a particular case of a general result about linear dependence versus independence for Gabor systems in $\ell^2(\mathbf Z)$ with modulation parameter $1/M$ and translation parameter $N$ for some $M,N\in \mathbf N,$ and generated by a finite sequence $g$ in $\ell^2(\mathbf Z)$ with $K$ nonzero entries.

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Ole Christensen, Marzieh Hasannasab. 2017-10-23. Gabor frames in $\ell^2(\mathbf Z)$ and linear dependence. https://arxiv.org/abs/1710.08280

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