Journal of Fourier Analysis and Applications

, Volume 25, Issue 1, pp 101–107 | Cite as

Gabor Frames in \({\ell }^2({\mathbb {Z}})\) and Linear Dependence

  • Ole ChristensenEmail author
  • Marzieh Hasannasab


We prove that an overcomplete Gabor frame in \({\ell }^2({\mathbb {Z}})\) generated 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 \({\ell }^2({\mathbb {Z}})\) with modulation parameter 1 / M and translation parameter N for some \(M,N\in {\mathbb {N}},\) and generated by a finite sequence g in \({\ell }^2({\mathbb {Z}})\) with K nonzero entries.


Frames Gabor system in \({\ell }^2({\mathbb {Z}})\) Linear dependency of Gabor systems 

Mathematics Subject Classification




The authors would like to thank Guido Janssen, Chris Heil and Shahaf Nitzan for useful comments and references.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.DTU ComputeTechnical University of DenmarkLyngbyDenmark

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