An Adaptive SVD Method for Solving the Pass-Region Problem in S-Transform Time-Frequency Filters

S-transform (ST) is an excellent tool for time-frequency filter. There are two factors that influence filtering performance: Inverse s-transform (IST) algorithms and the pass-regions in time-frequency domain. A novel matrix IST algorithm is derived and an adaptive Singular value decomposition (SVD) method for solving the pass-region problem is proposed. The former can avoid reconstructing errors in time-frequency filtering; the latter is effective to distinguish the pass-region of signal from noise. Filter can be realized by removing the smaller singular values and keeping the larger singular values. An additive noise perturbation model is built in ST time-frequency domain and the effective rank of noise perturbation model based on matrix IST is analyzed. Simulation results indicate that the proposed SVD method can provide higher precision than the existing ones at low signal-to-noise ratio and does not need to compute the noise statistics property. Illustrative examples verify the effectiveness of proposed method.