Sparse time-frequency representation based on multiwindow discrete Gabor transform

Abstract

The multiwindow discrete Gabor transform (M-DGT) is an important time-frequency analysis tool in many applications. In this paper, sparse time-frequency representation (TFR) based on M-DGT with sparse regularization theory is presented. The M-DGT is first formulated as a convex constrained optimization model by minimizing the objective function with a mixed [Formula: see text]–[Formula: see text] norm of the M-DGT coefficients. Then, an iterative algorithm based on the split Bergman method is utilized to compute the sparse Gabor time-frequency spectrum of the analyzed signal. According to the Heisenberg uncertainty principle, using an analysis window with good time resolution in M-DGT will lead to the Gabor TFR with high frequency resolution and vice versa. To obtain the sparse TFR with good time-frequency resolution (or concentration), the sparse spectra of M-DGT can be combined by the arithmetic average or the geometric average. Numerical experiments clearly show that the proposed method is an effective and powerful tool for analyzing nonstationary signals, by which the high time-frequency concentration (or resolution) of the Gabor time-frequency spectrum can be obtained as compared to traditional M-DGT.