## 3 Simulation Signal Analysis
At the same time, to visualize the effect of noise reduction in the proposed method in this paper, the time-frequency diagrams of the original signal without noise, the original signal with noise, the original signal with direct noise reduction, and the original signal with CEEMDAN decomposition and then noise reduction are made by using the STFT and CWT methods. The proposed improved SVD noise reduction singular value threshold screening method is used, and the preset thresholds in Equation (25) are set to 0.2 to reduce the IMF containing more noise after the improved CEEMDAN decomposition; the signal is then reconstructed. To quantitatively evaluate the noise reduction effect of different methods on the signals, the signal-to-noise ratio (SNR) index (Equation (27)) is introduced to compare the noise reduction effect of various methods, and the calculation results are shown in Table 2.  
\[R_{SN}=10\lg\frac{P_{\mathrm{s}}}{P_{\mathrm{n}}} \tag{27}\]  
where: \(P_{\mathrm{s}}\) is the sum of the effective power of the signal after noise reduction; \(P_{\mathrm{n}}\) is the sum of the effective power of the original signal. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Signal Type** & **Norm** & \begin{tabular}{c} **Before Noise** \\ **Reduction** \\ \end{tabular} & \begin{tabular}{c} **Improvement of the** \\ **CEEMDAN Method** \\ \end{tabular} & \
\begin{tabular}{c} **SVD Noise** \\ **Reduction** \\ \end{tabular} &
\begin{tabular}{c} **Methodology of** \\ **This Paper** \\ \end{tabular} \\ \hline Emulation signal & \(\mathrm{SNR/dB}\) & \(-12.9989\) & \(-7.4970\) & \(-2.4013\) & 0.9957 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: A comparison of the effect of each noise reduction method. Figure 5: A comparison of power spectra between Improved CEEMDAN and CEEMDAN decompositions. From Figure 6, it can be seen that after adding the noise signal with higher intensity, the original signal is completely covered by the noise signal, and no matter if the time-frequency diagrams are plotted using STFT or CWT methods, the regular original signal cannot be recognized in Figure 6c,d, as shown in Figure 6a,b. To provide a clearer and more intuitive assessment of the effectiveness of the joint noise reduction method, the figure below illustrates the time-domain graphs of the following signals: the noise-free test signal, the original signal containing noise, and the reconstructed signal obtained using the noise reduction method proposed in this paper. The graph clearly demonstrates the notable improvement achieved in reducing noise through the application of the proposed method. From Table 2, it can be seen that before the noise reduction process, the signal-to-noise ratio of the original signal after adding random white noise is \(-\)12.9989 dB; at this time, the signal is seriously distorted. By comparing, it can be seen that using Improved CEEMDAN denoising alone and using SVD denoising alone have certain denoising effects, with an improvement in SNR value. However, compared with the joint denoising of Improved CEEMDAN-SVD, the latter shows a significant increase in signal-to-noise ratio, reaching 0.9957 dB. This indicates that the joint denoising approach outperforms the individual denoising methods. From Figure 7, it can be seen that the feature signals around 4000 Hz are better extracted, but there is some noise retained near 2500 Hz and above 6000 Hz that is not filtered out. It shows that the SVD method alone cannot filter out the strong noise, and other methods need to be used to assist the analysis. Figure 8 shows the time-frequency diagram of the reconstructed noisy original signal after the improved CEEMDAN decomposition and SVD threshold noise reduction for each IMF, and it can be seen that the overall noise level of the signal after CEEMDAN decomposition and SVD threshold noise reduction for each IMF is reduced compared with the case in which the SVD threshold noise reduction is directly applied without CEEMDAN decomposition.