Gabor Frames for Model Sets
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DOI: 10.1007/s00041-019-09674-0
Abstract: We generalize three main concepts of Gabor analysis for lattices to the setting of model sets: fundamental identity of Gabor analysis, Janssen’s representation of the frame operator and Wexler–Raz biorthogonality relations. Utilizing the connection between… read more here.
Keywords: gabor frames; analysis; model sets; model ... See more keywords
Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials
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DOI: 10.1007/s00208-024-03011-7
Abstract: We introduce two families of generators (functions) G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {G}}$$\end{document} that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian… read more here.
Keywords: quasi shift; shift invariant; invariant spaces; shift ... See more keywords
On compactly supported dual windows of Gabor frames
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125436
Abstract: Abstract The main purpose of the paper is to give a characterization of all compactly supported dual windows of a Gabor frame. As an application, we consider an iterative procedure for approximation of the canonical… read more here.
Keywords: dual windows; gabor frames; compactly supported; supported dual ... See more keywords
Statistically Optimal Estimation of Signals in Modulation Spaces Using Gabor Frames
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DOI: 10.1109/tit.2022.3152734
Abstract: Time-frequency analysis deals with signals for which the underlying spectral characteristics change over time. The essential tool is the short-time Fourier transform, which localizes the Fourier transform in time by means of a window function.… read more here.
Keywords: time; fourier transform; gabor frames; signals modulation ... See more keywords
Extensions of Co-Compact Gabor Frames on Locally Compact Abelian Groups and Applications
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DOI: 10.4171/prims/61-4-4
Abstract: This paper addresses the extensions of co-compact Gabor Bessel sequences to tight frames and dual pairs on locally compact abelian (LCA) groups, and its applications to the L^{2}(\mathbb{R}^{d}) -setting. Firstly, we present a method to… read more here.
Keywords: compact gabor; locally compact; compact abelian; gabor ... See more keywords