Gabor frame bound optimizations
Functional Analysis
2025-04-28 v2 Classical Analysis and ODEs
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.
Cite
@article{arxiv.2204.02917,
title = {Gabor frame bound optimizations},
author = {Markus Faulhuber and Irina Shafkulovska},
journal= {arXiv preprint arXiv:2204.02917},
year = {2025}
}
Comments
32 pages, 15 figures + 1 figure in supplement, 53 references, 2 supplementary files. Significantly shortened to increase readability. Technical computations moved to supplementary file. To appear in Applied and Computational Harmonic Analysis