Algorithm for Finding the Best Linear Combination Window Under the Sparse Solution Constraint of Discrete Gabor Transform Coefficients

Single-window discrete Gabor transform with an adaptive window width selection algorithm (AWWS-DGT) and multi-window discrete Gabor transform (M-DGT) are the current mainstream analysis and processing methods for multi-component signals. However, the time-frequency accuracy in the time-frequency plane obtained by the two algorithms is not very high, and not all components of the signals that contain complex and very different time-frequency components can be displayed accurately. The linear combination window algorithm based on the l(1) and l(2) norm constraints of the transform coefficients can accurately display all the components of the signal, but the algorithm has poor anti-noise performance. In this paper, an algorithm for finding the best linear combination window under the sparse solution constraint of discrete Gabor transform coefficients is proposed. First, the optimal window number adaptive selection method proposed in this paper is used to select a set of window functions with different window widths, and the goal is to obtain the sparse solution of the transform coefficient. Through the gradient descent method, the best linear combination coefficient is obtained. Second, according to the best linear combination coefficient obtained, the selected window is combined into an analysis window function. Finally, the influence of the parameters on the combined window is further studied, and the results show that the number of windows has a great influence on the result and that the influence of the regularization parameter is negligible. Experiments on two simulated non-stationary signals and real electrocardiogram signals show that the proposed algorithm can display all components of the signals, the time-frequency accuracy is improved by 3% to 10%, and the anti-noise performance is more than 20% higher than that of the existing linear combination window algorithm. These advantages are very important for the analysis and processing of practical signals.