Gabor frame bound optimizations

Markus Faulhuber; Irina Shafkulovska

doi:10.48550/arXiv.2204.02917

Gabor frame bound optimizations

Markus Faulhuber, Irina Shafkulovska

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We study sharp frame bounds of Gabor systems over rectangular lattices for different windows and integer oversampling rate. In some cases we obtain optimality results for the square lattice, while in other cases the lattices optimizing the frame bounds and the condition number are rectangular lattices which are different for the respective quantities. Also, in some cases optimal lattices do not exist at all and a degenerated system is optimal.

Original language	English
Journal	Applied and Computational Harmonic Analysis
Volume	67
Early online date	13 Jul 2023
DOIs	https://doi.org/10.48550/arXiv.2204.02917 https://doi.org/10.1016/j.acha.2023.101574
Publication status	Published - 27 Jul 2023

Austrian Fields of Science 2012

101032 Functional analysis
101031 Approximation theory

Keywords

math.FA
math.CA
primary: 42C15, secondary: 26A06, 33B10

Access to Document

1 Finished
1 Active

Inside the Frame Set
Faulhuber, M.
1/03/21 → 28/02/25
Project: Research funding
Universal Optimality of the Hexagonal Lattice
Faulhuber, M.
1/10/20 → 30/09/22
Project: Research funding

1 Talk or oral contribution
1 Poster presentation

Gabor frame bound optimizations
Irina Shafkulovska (Speaker)
9 Apr 2024
Activity: Talks and presentations › Talk or oral contribution › Science to Science
Gabor Frame Bounds Optimizations
Irina Shafkulovska (Speaker)
23 Jun 2022
Activity: Talks and presentations › Poster presentation › Science to Science

Cite this

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title = "Gabor frame bound optimizations",

abstract = "We study sharp frame bounds of Gabor systems over rectangular lattices for different windows and integer oversampling rate. In some cases we obtain optimality results for the square lattice, while in other cases the lattices optimizing the frame bounds and the condition number are rectangular lattices which are different for the respective quantities. Also, in some cases optimal lattices do not exist at all and a degenerated system is optimal.",

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AB - We study sharp frame bounds of Gabor systems over rectangular lattices for different windows and integer oversampling rate. In some cases we obtain optimality results for the square lattice, while in other cases the lattices optimizing the frame bounds and the condition number are rectangular lattices which are different for the respective quantities. Also, in some cases optimal lattices do not exist at all and a degenerated system is optimal.

KW - math.FA

KW - math.CA

KW - primary: 42C15, secondary: 26A06, 33B10

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VL - 67

JO - Applied and Computational Harmonic Analysis

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ER -

Gabor frame bound optimizations

Abstract

Austrian Fields of Science 2012

Keywords

Access to Document

Projects

Inside the Frame Set

Universal Optimality of the Hexagonal Lattice

Activities

Gabor frame bound optimizations

Gabor Frame Bounds Optimizations

Cite this