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
KW - Banach frames
KW - Decomposition spaces
KW - Nonlinear approximation
KW - Nonstationary Gabor frames
KW - Time–frequency analysis
UR - http://www.scopus.com/inward/record.url?scp=85019038664&partnerID=8YFLogxK
U2 - 10.1007/s00041-017-9546-6
DO - 10.1007/s00041-017-9546-6
M3 - Journal article
SN - 1069-5869
VL - 24
SP - 1048
EP - 1071
JO - Journal of Fourier Analysis and Applications
JF - Journal of Fourier Analysis and Applications
IS - 4
ER -