## 4 Results and Discussion
### Short-Time Fourier Transform Implementation  
The filtering technique with the short-time Fourier transform is evaluated. Now, the transform, \(\mathcal{T}\), is \(STFT\) and, consequently, the transform variable, \(\chi\), is the pair frequency and window time instant. The received signal is composed of several dispersive waves distributed over time and in the frequency spectrum, as shown in Figure 4c. Since each wave packet may have different sensitivity to strain, a time-frequency representation, such as the short-time Fourier transform, should better identify different sensitivities. Initially, the \(M_{\phi,\ell}(\tau,f)\) function is computed. Figure 11 shows it for \(\phi=15^{\circ}\) and \(\phi=30^{\circ}\), where the white and black colors mean values zero and one, respectively. As \(\phi\) increases, fewer components are kept unfiltered (white spots), preserving only the ones that present high sensitivity to strain. The same principle as the \(FT\)-based filter holds here; the difference is that the components are identified in both frequency and time. The original signal is then filtered with the zero-one function, \(M_{\phi,\ell}(\tau,f)\), in order to eliminate the components that present low phase shift, resulting in the spectrum shown in Figure 12. The filtering technique has clearly altered the signal's spectrum and, consequently, the time-domain signal. Figure 13b,c shows the new focused signal, \(y_{\phi}(0,t)\), obtained with the \(STFT\)-based filter. Comparing it with Figure 8, one can see that the signal's shape is altered differently than with the Fourier transform filter, due to the different nature of both filtering procedures. The one based on \(STFT\) is able to discriminate different wave packets that share the same frequency. As a consequence, with the same value of \(\phi\), more components can be selected with the \(STFT\)-based filter compared to the \(FT\)-based filter. This also suggests that the TREF should be higher since more components can participate in the focusing. One can see that the signal level away from focus is indeed more intense when \(y_{\phi}(0,t)\) is obtained  
Figure 11: Time–frequency representation of \(M_{\phi,\ell}(\tau,f)\) at: (**a**) \(\phi=15^{\circ}\); and (**b**) \(\phi=30^{\circ}\). Black and white spots represent values zero and one, respectively. Figure 12: \(STFT\)–filtered reference signals in time–frequency domain \(H_{\phi,\ell}(\tau,f)\) (**a–c**) and in the time domain \(h_{\phi,\ell}(t)\) (**d–f**), with \(\phi=0^{\circ}\) (**a,d**), \(\phi=15^{\circ}\) (**b,e**), and \(\phi=30^{\circ}\) (**c,f**). Amplitude is normalized with respect to \(h(0,t)\). with _FT_-based filter than with the _STFT_ one. Table 1 summarizes the TREF for several values of \(\phi\). Figure 9 shows the amplitude reduction as a function of strain with _STFT_-based filtering for \(\phi=30^{\circ}\) (green dots). Table 1 summarizes the sensitivity for the same threshold angle as in the _FT_ case. The _STFT_-filter technique presents better results than the _FT_-filter one because it provides higher TREF and sensitivity for the same threshold angles. Figure 10 shows the behavior of the peak reduction sensitivity and TREF as a function of \(\phi\) with dashed lines. As can be seen, the TREF with _STFT_ approach is greater than or equal to the _FT_ approach, and the sensitivity is higher within the interval of \(\phi\) from \(20^{\circ}\) to \(60^{\circ}\), which is a region where TREF has not decreased severely, and thus a more useful region. At \(\phi=30^{\circ}\), the sensitivity with the _STFT_-based filter was 44.5% higher than with the _FT_-based one, the greatest relative difference between the techniques in this interval and about twice the sensitivity of the original procedure. In addition, the _STFT_ technique presents a much smoother TREF and sensitivity behavior than the _FT_ one. It is worth highlighting that common structural components are usually less simplistic than the experimental setup used here, presenting bolts, rivets, and welds, among other features.