A characterization of sparse nonstationary Gabor expansions

Research output: Contribution to journalJournal articleResearchpeer-review

3 Citations (Scopus)

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.
Original languageEnglish
JournalJournal of Fourier Analysis and Applications
Volume24
Issue number4
Pages (from-to)1048-1071
Number of pages24
ISSN1069-5869
DOIs
Publication statusPublished - Aug 2018

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Gabor Frames
Decomposition
Decompose
Banach Frames
Approximation Error
Coefficient
Thresholding
Upper bound
Norm

Cite this

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title = "A characterization of sparse nonstationary Gabor expansions",
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.",
keywords = "Time-frequency analysis, nonstationary Gabor frames, Decomposition spaces, Banach frames, Nonlinear approximation",
author = "Ottosen, {Emil Solsb{\ae}k} and Morten Nielsen",
year = "2018",
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doi = "10.1007/s00041-017-9546-6",
language = "English",
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pages = "1048--1071",
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A characterization of sparse nonstationary Gabor expansions. / Ottosen, Emil Solsbæk; Nielsen, Morten.

In: Journal of Fourier Analysis and Applications, Vol. 24, No. 4, 08.2018, p. 1048-1071.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - A characterization of sparse nonstationary Gabor expansions

AU - Ottosen, Emil Solsbæk

AU - Nielsen, Morten

PY - 2018/8

Y1 - 2018/8

N2 - 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.

AB - 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.

KW - Time-frequency analysis

KW - nonstationary Gabor frames

KW - Decomposition spaces

KW - Banach frames

KW - Nonlinear approximation

U2 - 10.1007/s00041-017-9546-6

DO - 10.1007/s00041-017-9546-6

M3 - Journal article

VL - 24

SP - 1048

EP - 1071

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

SN - 1069-5869

IS - 4

ER -