A characterization of sparse nonstationary Gabor expansions

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Abstract

We investigate the problem of constructing sparse time–frequency representations with flexible frequency resolution, studying the theory of nonstationary Gabor frames (NSGFs) in the framework of decomposition spaces. Given a painless NSGF, we construct a compatible decomposition space and prove that the NSGF forms a Banach frame for the decomposition space. Furthermore, we show that the decomposition space norm can be completely characterized by a sparseness condition on the frame coefficients and we prove an upper bound on the approximation error occurring when thresholding the frame coefficients for signals belonging to the decomposition space.
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We investigate the problem of constructing sparse time–frequency representations with flexible frequency resolution, studying the theory of nonstationary Gabor frames (NSGFs) in the framework of decomposition spaces. Given a painless NSGF, we construct a compatible decomposition space and prove that the NSGF forms a Banach frame for the decomposition space. Furthermore, we show that the decomposition space norm can be completely characterized by a sparseness condition on the frame coefficients and we prove an upper bound on the approximation error occurring when thresholding the frame coefficients for signals belonging to the decomposition space.
Original languageEnglish
JournalJournal of Fourier Analysis and Applications
Volume24
Issue number4
Pages (from-to)1048-1071
Number of pages24
ISSN1069-5869
DOI
StatePublished - Aug 2018
Publication categoryResearch
Peer-reviewedYes
ID: 257669377