TY - UNPB
T1 - A characterization of sparse nonstationary Gabor expansions
AU - Ottosen, Emil Solsbæk
AU - Nielsen, Morten
PY - 2016/6
Y1 - 2016/6
N2 - We investigate the problem of constructing sparse time-frequency representations with flexible frequency resolution, studying the theory of nonstationary Gabor frames in the framework of decomposition spaces. Given a painless nonstationary Gabor frame, we construct a compatible decomposition space and prove that the nonstationary Gabor frame 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 that occurs 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 in the framework of decomposition spaces. Given a painless nonstationary Gabor frame, we construct a compatible decomposition space and prove that the nonstationary Gabor frame 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 that occurs 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
M3 - Working paper
BT - A characterization of sparse nonstationary Gabor expansions
PB - arXiv
ER -