Gabor Frames in ℓ2(Z) and Linear Dependence

Ole Christensen*, Marzieh Hasannasab

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

We prove that an overcomplete Gabor frame in (Formula presented.) 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 (Formula presented.) with modulation parameter 1 / M and translation parameter N for some (Formula presented.) and generated by a finite sequence g in (Formula presented.) with K nonzero entries.
Original languageEnglish
JournalJournal of Fourier Analysis and Applications
Volume25
Issue number1
Pages (from-to)101–107
ISSN1069-5869
DOIs
Publication statusPublished - 2018

Keywords

  • Frames
  • Gabor system in $${\ell }^2({\mathbb {Z}})$$ℓ2(Z)
  • Linear dependency of Gabor systems

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