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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Detaljer

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.
OriginalsprogEngelsk
TidsskriftJournal of Fourier Analysis and Applications
Volume/Bind24
Tidsskriftsnummer4
Sider (fra-til)1048-1071
Antal sider24
ISSN1069-5869
DOI
StatusUdgivet - aug. 2018
PublikationsartForskning
Peer reviewJa

    Forskningsområder

  • Time-frequency analysis, nonstationary Gabor frames, Decomposition spaces, Banach frames, Nonlinear approximation
ID: 257669377