## 4 Results and Discussion
### Fourier Transform Filter Implementation
To quantify the sensitivity, the angular coefficient of a linear fit of the experimental peak decrease was calculated and is shown as the continuous lines in Figure 9. These values are reported in Table 1, where the first row, referred to \(\phi=0^{\circ}\), presents the results obtained without any filtering. The sensitivity is reported through the mean and standard deviation (std.) of the angular coefficient. These values were calculated considering four loading experiment, where each one contains at least five acquisitions for each evaluated strain value. The TREF values, in percent, for the focused signal at null strain, shown in Figure 8, are also reported in Table 1. As can be seen, the increase of sensitivity comes at a price, as the energy focusing efficiency decreased, i.e., lower TREF was obtained. It is worth noting that the TREF values in Table 1 were computed considering the whole acquisition window shown in Figures 5 and 8 to calculate the energy in the denominator of Equation (2). This time window encompasses almost all the non-negligible amplitude. If a narrower acquisition window around the peak were used, higher values would be found, but the same overall behavior with the increase of \(\phi\) would be obtained. The amplitude sensitivity and the TREF behavior as a function of the threshold angle \(\phi\) are shown in Figure 10 by the continuous lines. One can see that, as \(\phi\) increases, sensitivity increases, until about 70\({}^{\circ}\) where it reaches about 0.6\(\%/\mu\epsilon\), approximately fivefold the original value. However, TREF tends to decrease almost monotonically. At about 70\({}^{\circ}\), TREF is just 1.25%, an extremely low value, meaning that the reference signal is so altered that it no longer correlates with the system's impulse response. Signals with very poor energy concentration compromise monitoring through peak observation since it may not produce a clearly identifiable main peak. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**FT\(-\)Filtering**} & \multicolumn{3}{c}{**STFT\(-\)Filtering**} \\ \cline{2-7} \(\phi\) & \multirow{2}{*}{**TREF**} & \multicolumn{2}{c}{**Peak Sensitivity**} & \multicolumn{2}{c}{**Peak Sensitivity**} \\ \cline{3-6} (deg.) & & **Mean** & **Std.** & **(\%)** & **Mean** & **Std.** \\  & & (\%/\(\mu\epsilon\)) & (\%/\(\mu\epsilon\)) & & (\%/\(\mu\epsilon\)) & (\%/\(\mu\epsilon\)) \\ \hline
0\({}^{\circ}\) & 11.96 & 0.1261 & 0.0009 & 11.96 & 0.1261 & 0.0009 \\ \hline
15\({}^{\circ}\) & 7.67 & 0.1345 & 0.0011 & 8.46 & 0.1369 & 0.0010 \\ \hline
30\({}^{\circ}\) & 4.69 & 0.1635 & 0.0016 & 6.28 & 0.2363 & 0.0020 \\ \hline
60\({}^{\circ}\) & 2.11 & 0.5064 & 0.0044 & 2.26 & 0.5074 & 0.0048 \\ \hline \end{tabular}
\end{table} 
Table 1: Sensitivity and TREF for _FT_ and _STFT_ filtering. Figure 10: Peak sensitivity (**a**) and TREF (**b**) as a function of \(\phi\) for _FT_ and _STFT_\(-\)filtering. Figure 9: Peak decrease as a function of strain for _FT_ and _STFT_ filtering. Symbols are experimental measure and lines are their linear fit. Error bar stands for at least five repeated experimental acquisitions at each strain level. Blue symbols and line indicate measurements without filtering (\(\phi=0^{\circ}\)), red symbols and line indicate reference signal obtained with _FT_\(-\)filtering, and green symbols and line indicate reference signal obtained with _STFT_\(-\)filtering. Both filtering methods were calculated with \(\phi=30^{\circ}\).