A Characterization of Sparse Nonstationary Gabor Expansions

作者：Ottosen Emil Sol**aek^*; Nielsen Morten

来源：Journal of Fourier Analysis and Applications, 2018, 24(4): 1048-1071.

DOI：10.1007/s00041-017-9546-6

• Time-frequency analysis
• Nonstationary Gabor frames
• Decomposition spaces
• Banach frames
• Nonlinear approximation

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.

• 出版日期2018-8