## 5 Application Results and Analysis
### Simulated Signal  
In order to simulate well the signal in the field, the simulated signals are composed of pulses with different waveforms by controlling the pulse parameters, as shown in Table 1. Signal \(s_{1}\) is formed by pulses P1-P5 and \(s_{2}\) is formed by pulses P6-P10. White noises are added to \(s_{1}\) and \(s_{2}\) so that the SNRs are equal to \(-5\) dB; the original signal and the noised signal are presented in Figure 5. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Signal**} & \multicolumn{4}{c}{\(\mathbf{S_{1}}\)} & \multicolumn{4}{c}{\(\mathbf{S_{2}}\)} \\ \hline Pulse & P1 & P2 & P3 & P4 & P5 & P6 & P7 & P8 & P9 & P10 \\ \hline A/mV & 8 & 13 & 12 & 18 & 35 & 15 & 10 & 20 & 8 & 8 \\ \hline \(\tau_{1}\)/\(\mu\)s & 3 & 3 & 2.5 & 0.25 & 0.9 & 0.75 & 0.8 & 0.8 & 1.8 & 2.5 \\ \hline \(\tau_{2}\)/\(\mu\)s & 0.5 & 0.5 & 0.3 & 0.08 & 0.7 & 0.1 & 0.1 & 0.1 & 0.3 & 0.3 \\ \hline \(f_{c}\)/MHz & – & 0.2 & 1.5 & 2.8 & 1.95 & 2.2 & 4.9 & 0.36 & 0.56 & 1.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the pulses. The noised signals are denoised by EBWS, SNRBWS, NewEBWS and the proposed method. According to the method described in the previous section, the decomposition levels of \(s_{1}\) and \(s_{2}\) are determined as 9 and 7 respectively. The denoising results of \(s_{1}\) and \(s_{2}\) can be compared in Figures 6 and 7. To display the pulse details clearly, the sections of pulses are cut out from the whole signal and the time axis densities of different pulses are different. As can be seen from the denoising results, the proposed method possesses smaller waveform distortion and higher waveform fidelity, which is particularly obvious for pulses P3, P4, P5, P7 and P10. The overall denoising performance of the proposed method is better than the other three methods. Besides, SNRBWS is more focused on the pulses with large amplitude, it performs poorer in the denoising of pulses with small amplitude. Figure 5: Original and noised signal (**a**)\(s_{1}\) (**b**)\(s_{2}\). Figure 6: Denoising result of pulses in \(s_{1}\) (**a**) noised and original signal (**b**) EBWS (**c**) SNRBWS (**d**) NewEBWS (**e**) the proposed method. To eliminate the stochastic behaviors and obtain statistical comparison results of different denoising methods, 1000 sets of different white noises are adopted; and the mean value of denoising evaluation indexes are shown in Table 2. It can be seen from the values of evaluation indexes that the proposed method performs best in denoising both \(s_{1}\) and \(s_{2}\). According to the principles of the proposed method, it is more time-consuming than other energy based wavelet selection methods because of the threshold estimation for each candidate mother wavelet at each scale. For the four methods, the time consumption of optimum mother wavelet selection and total computation time of denoising are calculated, respectively, and the comparisons are shown in Figure 8 in the form of a stick chart. The time comparison results in Figure 8 indicate that the proposed mother wavelet selection method is more time-consuming. However, as can be seen from Figure 8, the total computation time of denoising depends little on the time consumption of optimum mother wavelet selection; the proposed scheme is comparable with existing methods with regard to time consumption. The times at each method obtain the best result for each denoising evaluation index are counted; the percentages are shown in Figure 9 in the form of pie charts. It is apparent that the proposed method possesses an obvious advantage over the other three methods. On the other hand, it indicates that no method can perform the best in all cases; SNRBWS also achieves the best in many cases and is only inferior to the proposed method.