Gabor systems with Hermite functions of order $$N$$ and oversampling greater than $$N+1$$ which are not frames

Abstract We show that a sufficient density condition for Gabor systems with Hermite functions over lattices is not sufficient in general. This follows from a result on how zeros of the Zak transform determine the frame property of integer over-sampled Gabor systems.

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Publication Details

Journal
Sampling Theory Signal Processing and Data Analysis
Published
2025-09-09
DOI
https://doi.org/10.1007/s43670-025-00112-5
Primary Topic
Mathematical Analysis and Transform Methods
Type
article
Field-Weighted Citation Impact
0.00

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article

Gabor systems with Hermite functions of order $$N$$ and oversampling greater than $$N+1$$ which are not frames

Markus Faulhuber
Sampling Theory Signal Processing and Data Analysis
Mathematical Analysis and Transform Methods
article

Gabor systems with Hermite functions of order $$N$$ and oversampling greater than $$N+1$$ which are not frames

Markus Faulhuber
article en

Abstract

Abstract We show that a sufficient density condition for Gabor systems with Hermite functions over lattices is not sufficient in general. This follows from a result on how zeros of the Zak transform determine the frame property of integer over-sampled Gabor systems.

Sampling Theory Signal Processing and Data AnalysisVol. 23(2)
University of Vienna (AT)
Austrian Science Fund, Universität Wien
Openalex Percentile: Top 65%
Mathematical Analysis and Transform Methods
DOIOpen Access PDFOpenAlex
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Gabor systems with Hermite functions of order $N$ and oversampling greater than $N+1$ which are not frames — Markus Faulhuber · Sampling Theory Signal Processing and Data Analysis (2025) | TGRS Research Map | TGRS