Robust time-varying filtering and separation of some nonstationary signals in low SNR environments

Conventional time-varying filtering is inefficient for severely spoiled signals because it requires discernible spectral content of the signal in time-frequency domain. Motivated by the time-frequency peak filtering (TFPF) algorithm, a robust time-varying filtering (RTVF) algorithm is proposed in this paper for the objectives of filtering and separating some nonstationary signals that contain strong noise. The performance of the TFPF based on windowed Wigner-Ville distribution is intrinsically limited by the linear constraint on the waveform of the received signal. The proposed RTVF significantly improves the filtering performance with low complexity by applying a sinusoidal time-frequency distribution, which allows a sinusoidal constraint on the signal׳s waveform. The bias analysis of the RTVF is presented for some nonstationary signals with time-varying amplitude. Based on derived bias expressions, a criterion of optimal window size selection for implementation purpose is obtained. The RTVF can successfully decompose some multi-component signal into individual components based on an initial instantaneous frequency (IF) estimate of each component. Unlike existing time-varying filters, the RTVF is much less sensitive to the accuracy of the initial IF estimate. Computer simulations verify the theoretical analysis and demonstrate that the RTVF algorithm can achieve desirable performance of filtering and separation in low SNR environments.