## 5 Application Results and Analysis
### Simulated Signal
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Signal** & \multicolumn{3}{c}{\(\mathbf{s_{1}}\)} & \multicolumn{3}{c}{\(\mathbf{s_{2}}\)} \\ \hline Indexes & MSE & NCC & MAE & MSE & NCC & MAE \\ \hline EBWS & 0.1129 & 0.9208 & 0.1783 & 0.0815 & 0.9145 & 0.1078 \\ \hline SNRBWS & 0.0950 & 0.9338 & 0.1722 & 0.0836 & 0.9122 & 0.1025 \\ \hline NewEBWS & 0.1040 & 0.9273 & 0.1749 & 0.0820 & 0.9139 & 0.1036 \\ \hline Proposed & 0.0906 & 0.9381 & 0.1420 & 0.0732 & 0.9249 & 0.0908 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean value of denoising evaluation indexes. Figure 7: Denoising result of pulses in \(s_{2}\)(**a**) noised and original signal (**b**) EBWS (**c**) SNRBWS (**d**) NewEBWS (**e**) the proposed method. To investigate the denoising effect for signals with different SNRs, white noise with different energy are added to \(s_{1}\) and \(s_{2}\) to make the SNRs vary from \(-5\) to \(5\) with a step of \(0.5\). To eliminate the stochastic behaviors and get the statistical comparison results of different denoising methods, \(100\) sets of different white noise are adopted for signals under each SNR, and the mean values of denoising evaluation indexes are employed. The relationships of denoising evaluation indexes with SNRs are presented in Figure 10. As can be seen, the denoising evaluation indexes of the proposed method are better than that of the compared methods. Through comprehensive analysis and evaluation, the proposed method performs well in the denoising of noised PD signals. From Figures 6 and 7, it can be seen that the denoised signals obtained by EBWS and NewEBWS show high similarity. By comparing the principles of the EBWS and NewEBWS, it can be seen that the criteria of wavelet selection are equivalent when the energy of approximation coefficients is larger than that of detail coefficients at all scales. If the energy of approximation coefficients is smaller than that of detail coefficients at a certain scale, EBWS will spread the wavelet coefficients energy, which is likely to result in more energy loss than NewEBWS does when the threshold is applied to the detail coefficients. is suitable for the pulse that the coefficient with maximum absolute value belongs to, and may not be suitable for the other pulses. As a consequence, if the energy proportion of the coefficient with maximum absolute value to all coefficients is very small, the denoising performance will be worse than the proposed method and NewEBWS. To verify the inference, simulated signal \(s_{3}\) is composed of pulses P1-P10, as shown in Figure 11.  
Signal \(s_{3}\) contains more pulses than \(s_{1}\) and \(s_{2}\), indicating that the mother wavelet selected by SNRBWS may be unsuitable for more pulses. One thousand sets of different white noises are adopted and the SNRs are all equal to \(-5\); the mean values of denoising evaluation indexes are presented in Table 3. As can be seen, the proposed method achieves the best performance in all three evaluation indexes. The statistical results of each method obtaining the best result for each evaluation index are shown in Figure 12; the times percentage of the proposed method are the best--are more than 60%--which is an absolute advantage over other three methods. By comparing the pie charts in Figure 12 with Figure 9, it can be concluded that the proposed method has a higher stability and adaptability, and is  
Figure 11: Original and noised signal of \(s_{3}\). Figure 10: The relationships between the mean values of denoising evaluation indexes and SNRs (**a**) \(s_{1}\) (**b**) \(s_{2}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Signal** & \multicolumn{3}{c}{\(\mathbf{S_{3}}\)} \\ \hline Index & MSE & NCC & MAE \\ \hline EBWS & 0.2857 & 0.8763 & 0.1116 \\ \hline SNRBWS & 0.2936 & 0.8729 & 0.1144 \\ \hline NewEBWS & 0.2553 & 0.8904 & 0.1033 \\ \hline Proposed & 0.2368 & 0.9001 & 0.0966 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean value of denoising evaluation indexes for \(s_{3}\). more suitable for the denoising of complicated PD signals.