## 4 Filter Parameters Analysis  
In order to be consistent with the real UGW testing signal, it is necessary to multiply the amplitude of the L(0,1) + F(_n_,1) + L(0,2) + F(_n_,3) synthesized signal with the propagation distance of 0.8 m by 0.6 as a defect echo, and the L(0,1) + F(_n_,1) + L(0,2) + F(_n_,3) synthesized signal with the propagation distance of 1.8 m is regarded as an end-reflected echo, as illustrated in Figure 7. Likewise, the resolution of the L(0,2) UGW will still be poor in the time-frequency domain because of the influence of other UGWs, and it is necessary to eliminate the coherent noise. The SSPs based on GS, RC, FBR-GS and FBR-RC filters (\(B=B_{3 dB}\), \(B_{\text{/GS}}=B_{\text{/RC}}=B_{3 dB}/10\), \(\Delta f=B_{3 dB}/40\), where \(B_{3 dB}\) is the 3 dB bandwidth of unprocessed signal) are used to process the synthesized UGW signal, and the results are shown in Figure 8. It can be found that the interpretation accuracy improvement of NORM-MIN and MEAN are not significant, of which the coherent noise is not completely eliminated. Although FM can effectively improve SNR, it also eliminates the defect echo, which is inadvisable. PT, PTM and SPT show excellent processing effects, where the defect echoes are retained and coherent noise is eliminated. In addition, it can also be observed that FBR-SSPs are better than SSPs, which is consistent with the discussion in Section 2.1. In order to achieve the best processing effect, it is necessary to choose the appropriate filter parameters for the parameter sensitivity of the SSP. The signal-to-noise ratio gain SNRG and defect-to-coherent noise gain DCRG are introduced to quantitatively measure the effects of parameters, of which the calculation formulas are as follows:  
\[SNRG=20\left[\log_{10}(S_{out}/N_{out})-\log_{10}(S_{in}/N_{in})\right] \tag{10}\]  
\[DCRG=20\left[\log_{10}(D_{out}/N_{out})-\log_{10}(D_{in}/N_{in})\right] \tag{11}\]  
Figure 8: Synthesized UGW signals before and after applying SSPs based on GS, RC, FBR-GS and FBR-RC filters. Figure 7: (**a**) Time and (**b**) frequency domain diagrams of the synthesized UGW signal. where \(S\) is the maximum amplitude of the signal, \(D\) is the amplitude of the defect echo, \(N\) is the coherent noise level calculated by the root mean square of the whole signal, and subscripts \(in\) and \(out\) represent before and after the SSP processing, respectively. The effects of \(B\) (\(k_{B}=B/B_{3 dB}\)) on SNRG and DCRG are shown in Figure 9a, where \(B_{t}=B_{3 dB}/10\), \(B_{r}=B_{3 dB}/20\) and \(\Delta f=B_{3 dB}/40\). The desired UGW mode and coherent noise components will be missed in \(X_{i}(f)\) if \(B\) is too small, so SNRG and DCRG tend to increase basically as \(B\) increases. However, PT and PTM with a good processing effect failed when \(k_{B}>2.2\), and the phenomenon that DCRG is greater than SNRG appears in PTM and SPT. Taking \(k_{B}=1.7\) as an example (the processed signals are shown in the dotted boxes), it can be found that the amplitudes of defect echoes are much larger than those of end-reflected echoes in spite of eliminating almost all the coherent noise, which is harmful to quantitative analysis of defect size. The above situation should be avoided while ensuring high SNRG and DCRG, so the appropriate \(k_{B}\) is 2 (\(B=2B_{3 dB}\)). In this way, the effects of \(B_{t}\), \(B_{r}\) and \(\Delta f\) on the SNRG and DCRG are illustrated in Figure 9b-d. It can be seen that the SNRG and DCRG are low when \(B_{t}\) and \(\Delta f\) are too big, which can be attributed to the great cross-correlation coefficient of adjacent filters and the missing desired mode UGW component in \(X_{i}(f)\). Therefore, \(B_{t}\) and \(\Delta f\) with too small of a value are not recommended; it is suitable to choose \(B_{t}=B/16\) and \(\Delta f=(2B_{t}+B_{r})/4\). In addition, the curves of SNRG and DCRG affected by \(B_{r}\) show different trends compared with those of \(B_{t}\) and \(\Delta f\).