Weighted multiwindow discrete Gabor transform

According to the Heisenberg uncertainty principle, an analysis window with a high time resolution in time domain will result in a low frequency resolution in frequency domain, and vice versa. To obtain the Gabor spectrum with high time-frequency resolution and concentration, weighted multiwindow discrete Gabor transform (M-DGT) using weights and the biorthogonal analysis method for analyzing long (or infinite) sequences is proposed in this paper, in which the combined Gabor coefficients constructed by a combination of M-DGT coefficients can be adaptively changed according to the time-frequency distributions of an analyzed signal containing multiple time-varying frequencies. To obtain the weights of the weighted M-DGT, the M-DGT is converted into a sparse problem with l(1)-l(2) regularization, then an efficient iterative algorithm for solving the weights in terms of real-valued matrix and real-valued vector is derived. The convergence of the iterative algorithm is proved by optimization theory. The experimental results demonstrate that the proposed method is an effective and efficient tool for nonstationary timefrequency analysis of signals. (C) 2021 Elsevier Inc. All rights reserved.