An open question on the existence of Gabor frames in general linear position

2009/01/01 by Felix Krahmer, Krahmer, Felix, Götz E. Pfander +3
Computer Science · Mathematics · #Digital Filter Design and Implementation #Gabor systems #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #erasure channels #short--time Fourier transform #time--frequency dictionaries #uncertainty principle.

paper · doi:10.4230/dagsemproc.08492.4

openalex publication_date 2009/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Uncertainty principles for functions defined on finite Abelian groups generally relate the cardinality of a function to the cardinality of its Fourier transform. We examine how the cardinality of a function is related to the cardinality of its short--time Fourier transform. We illustrate that for some cyclic groups of small order, both, the Fourier and the short--time Fourier case, show a remarkable resemblance. We pose the question whether this correspondence holds for all cyclic groups.

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