## 3 Results  
To illustrate the effectiveness of the proposed method in comparison with the conventional amplitude threshold trigger, we constructed two sets of testing signals: the small set of eight equally spaced AE transients and the large one having one thousand AE pulses buried into background noise with random time intervals between the events. To produce these synthetic datasets, we have arbitrarily chosen typical realisations of AE transient waveforms with significantly different amplitudes and durations, which were acquired by the NF-900S-WB (NF Electronics, Yokohama, Japan) wide-band AE sensor during plastic deformation of \(\alpha\)-Fe in tension at the sampling rate 2 Msamples/s and 16 bits resolution, as shown in Figure 2.  
These waveforms were buried into the actual scalable background noise 0.005 s apart from one another, as shown in Figure 3. The noise data represents the actual coloured electronic noise from the pre-amplifier. It was recorded with the same experimental setup, including the sensor connected to the pre-amplifier. SNR values for each of the five chosen noise levels and for each of the eight events are shown in Table 1. For the larger dataset, one thousand waveforms representing a Poisson time series with random independent intervals between each other were embedded into the same noise. Fragments of this dataset with different tested noise levels are shown in Figure 4.  
Figure 3: The synthetic dataset containing eight real AE signals shown in Figure 2 and embedded into real scalable background noise with different levels labelled by numbers from 1 to 5. The dashed vertical lines indicate the positions of the signals. Figure 2: Typical acoustic emission waveforms with different amplitudes and durations, which were randomly chosen from continuously recorded data acquired at 2 Msamples/s rate. The PSD plugged into Equation (3) was calculated by the Welch periodogram method. Minimum and maximum frequencies in this equation are determined by the frequency band of the sensor used, which is of 0.1-1.0 MHz for the general-purpose AE sensors. Thus, having the sampling frequency of the acquisition system of 2 MHz, the integration is performed from 0.1 to 1 MHz. Values of all parameters used in the \(\phi\)-signal detector are listed in Table 2. One can notice, for example, that the time shift \(s\) is chosen greater than the size of the smoothing window \(M\), as has been discussed above. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Noise Level**} & \multicolumn{8}{c}{**Number of Event**} \\ \cline{2-9}  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline
1 & 6.0 & 7.2 & 7.8 & 4.2 & 3.7 & 21.5 & 6.8 & 4.3 \\
2 & 0 & 1.2 & 1.8 & \(-\)1.9 & \(-\)2.3 & 15.5 & 0.8 & \(-\)1.7 \\
3 & \(-\)3.5 & \(-\)2.3 & \(-\)1.7 & \(-\)5.4 & \(-\)5.9 & 12.0 & \(-\)2.7 & \(-\)5.2 \\
4 & \(-\)6.5 & \(-\)4.8 & \(-\)4.2 & \(-\)7.9 & \(-\)8.4 & 9.5 & \(-\)5.2 & \(-\)7.7 \\
5 & \(-\)8.0 & \(-\)6.7 & \(-\)6.2 & \(-\)9.8 & \(-\)10.3 & 7.5 & \(-\)7.2 & \(-\)9.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Signal-to-noise ratio for different signals from Figure 3 (dB). Figure 4: The fragment of the synthetic dataset containing totally 1000 AE signals embedded into background noise with different levels labelled by numbers from 1 to 5. Since in the present work, the number of true events is known a priori, the detection completeness is estimated as shown in Tables 3 and 4. For all methods tested, the parameters were set to provide maximum detection and minimum false alarm probabilities. We should mention here that unlike many phase-picking algorithms, such as that reported in [19] for example, the proposed method has few parameters, all of which are intuitively understandable and not difficult to set (in a way similar to those in the LTA/STA procedure).