## 4 Performance Analysis
### Simulation Performance Analysis
#### 4.1.2 Extracting Time-Frequency Features from Simulation Signals  
The disturbing signal was subjected to short-time Fourier transform, continuous wavelet transform, and synchrosqueezed wavelet transform, respectively, to extract power spectra. \"Bump\" wavelet was adopted by both wavelet methods, as shown in Figure 3:  
From the generation of the simulation signal and the analysis of the above figure, it can be observed that the short-time Fourier transform and the continuous wavelet transform does not have good time-frequency resolution and cannot effectively display the change of the target signal in the time-resolved spectra while the synchrosqueezed wavelet transform can better concentrate the energy near the real energy axis, and the signal weakens significantly when the target passes through (that is, it turns from the yellow color of strong energy to the blue color of weak energy). The simulation signal also effectively proves the feasibility of the power frequency magnetic anomaly detection technology, that is, the magnetic field around the observation point will be affected by the movement of ferromagnetic targets.  
Intending to obtain a quantitative and intuitive evaluation and comparison of the advantages of several different methods for time-frequency analysis, this paper denoises the simulated magnetic anomaly signals generated above and produces the Rayleigh quotient values corresponding to the three time-frequency analysis methods under different signal-to-noise ratios in Figure 3, as shown in Table 1:  
The smaller the Rayleigh entropy, the higher is the time-frequency aggregation. As shown in Table 1, the synchrosqueezed wavelet transform spectrum is significantly superior to the latter two in time-frequency resolution, and the synchrosqueezed wavelet transform that generates time-frequency has the smallest Rayleigh quotient.  
Meanwhile, this paper compares the performance of four different mother wavelets in the synchrosqueezed wavelet transform: Gauss, Bump, Cmhat, and Morlet, and uses the calculation of the corresponding Rayleigh entropy values of different mother wavelets under different signal-to-noise conditions to judge the advantages and disadvantages of different wavelet bases, the results of which are shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Time-Frequency Analysis Method** & **SNR = 0 db** & **SNR = 5 db** & **SNR = 10 db** & **SNR = 15 db** \\ \hline CWT & 7.0825 & 6.8863 & 5.8225 & 5.3125 \\ STFT & 7.2562 & 6.9525 & 5.8956 & 5.6245 \\ SSWT & 2.8939 & 2.7960 & 1.9572 & 1.6572 \\ \hline \end{tabular}
\end{table}
Table 1: Rayleigh entropy comparison of different time-frequency analysis methods under different noise conditions.  
Figure 3: The simulation data using STFT, CWT, and SSWT processing time-frequency diagram; (**a**–**c**) are STFT, CWT, and SSWT images.  
The table demonstrates that the synchrosqueezed wavelet transform method has better time-frequency resolution when using the \"Morlet\" and \"Bump\" mother wavelets. When \"Morlet\" and \"Bump\" are compared, Bump has a better time-frequency resolution. Therefore, this paper mainly uses the Bump wavelet as the mother wavelet function. In addition, the Bump wavelet has the best performance on the image, and we will put the image comparison between the Bump wavelet and Morlet wavelet in the measured data in Section 4.2.2.  
The contours are extracted from three time-spectrum types at the same time to extract the disturbance signal's features more effectively, as shown in Figure 4:  
As shown in the enlarged image in Figure 4, the Synchrosqueezing Transform more effectively preserves the features of the magnetic anomaly signal resulting from the target's movement, and its contour distribution indicates a more profound change, which can better represent the target-induced disturbance signal.