On the reconstruction of nonsparse time-frequency signals with sparsity constraint from a reduced set of samples

摘要

Nonstationary signals, approximately sparse in the joint time-frequency domain, are considered. Reconstruction of such signals with sparsity constraint is analyzed in this paper. The short-time Fourier transform (STFT) and time-frequency representations that can be calculated using the STFT are considered. The formula for error caused by the nonreconstructed coefficients is derived and presented in the form of a theorem. The results are examined statistically on examples.