Time-frequency peak filtering (TFPF) may efficiently suppress random noise and hence improve the signal-to-noise ratio. However, the errors are not always satisfactory when applying the TFPF to fast-varying seismic signals. We begin with an error analysis for the TFPF by using the spread factor of the phase and cumulants of noise. This analysis shows that the nonlinear signal component and non-Gaussian random noise lead to the deviation of the pseudo-Wigner-Ville distribution (PWVD) peaks from the instantaneous frequency. The deviation introduces the signal distortion and random oscillations in the result of the TFPF. We propose a weighted reassigned smoothed PWVD with less deviation than PWVD. The proposed method adopts a frequency window to smooth away the residual oscillations in the PWVD, and incorporates a weight function in the reassignment which sharpens the time-frequency distribution for reducing the deviation. Because the weight function is determined by the lateral coherence of seismic data, the smoothed PWVD is assigned to the accurate instantaneous frequency for desired signal components by weighted frequency reassignment. As a result, the TFPF based on the weighted reassigned PWVD (TFPF_WR) can be more effective in suppressing random noise and preserving signal as compared with the TFPF using the PWVD. We test the proposed method on synthetic and field seismic data, and compare it with a wavelet-transform method and [Formula: see text] prediction filter. The results show that the proposed method provides better performance over the other methods in signal preserving under low signal-to-noise ratio.
Theory and Measurement of Signal-to-Noise Ratio in Continuous-Wave Noise Radar
