2013/11/30 by Karlheinz Gröchenig, Joaquim Ortega‐Cerdà, Joaquim Ortega-Cerdà +1 · 58 citations
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Bandlimiting #Characterization (materials science) #Computer science #Computer vision #Deformation (meteorology) #Fourier transform #Gabor transform #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Nonlinear system #Optics #Pure mathematics #Time–frequency analysis #math.FA #msc:42C15 #msc:42C30 #msc:42C40
paper · pdf · doi:10.1016/j.aim.2015.01.019
published in Advances in Mathematics 277, 388-425 (Elsevier BV) · 31 pages, 2 figures
arxiv created 2015/03/23 · openalex publication_date 2015/03/31 · arxiv updated 2016/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We introduce a new notion for the deformation of Gabor systems. Such deformations are in general nonlinear and, in particular, include the standard jitter error and linear deformations of phase space. With this new notion we prove a strong deformation result for Gabor frames and Gabor Riesz sequences that covers the known perturbation and deformation results. Our proof of the deformation theorem requires a new characterization of Gabor frames and Gabor Riesz sequences. It is in the style of Beurling's characterization of sets of sampling for bandlimited functions and extends significantly the known characterization of Gabor frames "without inequalities" from lattices to non-uniform sets.