Linear independence and coherence of Gabor systems in finite dimensional spaces

Götz Pfander (1)

1 JU-SES - School of Engineering and Science [Bremen]

This paper reviews recent results on the geometry of Gabor systems in finite dimensions. For example, we discuss the coherence of Gabor systems, the linear independence of subsets of Gabor systems, and the condition number of matrices formed by a small number of vectors from a Gabor system. We state a result on the recovery of signals that have a sparse representation in certain Gabor systems. The results listed here are obtained by the author in collaborations with Jim Lawrence, Felix Krahmer, Peter Rashkov, Jared Tanner, Holger Rauhut, and David Walnut

Domaines: Analyse fonctionnelle [math.FA]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Götz Pfander. Linear independence and coherence of Gabor systems in finite dimensional spaces. SAMPTA'09, May 2009, Marseille, France. Special Session on frame theory and oversampling. ⟨hal-00451606⟩