Simple Threshold Detectors

Figure 5.13 shows the ROC curve for the TEO detector. As it has been men-tioned, the Teager Energy Operator acts as a non-linear high-pass filter attenu-ating low frequency background noise. Impulse noise is characterized for being broadband, hence when extracting the TEO feature from a train track noise measurement, the low frequency background is expected to be attenuated while the high frequency components of any present transient events are preserved.

In this way, the TEO detector is able to produce high AU C(0.2) as shown in figure 5.13.

Figure 5.13: TEO detector ROC curve.

Figure 5.14 shows the ROC curves for the TEOFREQ detector. Note how an analysis in frequency bands does not improve the AU C(0.2), on the contrary, it is decreased. The TEOFREQ detector filters a signal in frequency bands.

At each frame it calculates the TEO feature values and normalizes that result to its RMS value. For low frequency bands, the TEO feature produces low value results as the high frequency components have been filtered out of the signal. Recall that the TEO acts as non-linear high-pass filter. Thus, after normalization to RMS, the window segment contains high levels of noise. For high frequency bands, the TEO feature is able to produce more accurate results as high frequency components are still present in the signal. From figure 5.14, it can also be observed how the or detection strategy performs worse than the anddetection strategy. This happens because low frequency bands contain high levels of noise, thus, the or strategy tends to yield more false positive results when no transient events are present in the signal. While the and strategy encourages the detector to yield true positives only when there are high values of the TEO normalized feature in higher frequency bands.

5.1 ROC results 71

(a)TEOFREQ detector ROC, and detection strategy.

(b)TEOFREQ detector ROC, or detection strategy.

Figure 5.14: TEOFREQ detector ROC curves.

Figure 5.15 shows the ROC curves for theCOE detector. Note how an increase of the parameter dimproves theAU C(0.2)up to a certain value, and then the AU C(0.2) decreases. This could be related to the duration of transient events, however it remains unclear how to find an optimaldparameter.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 5.15: COE detector ROC curves.

2 4 6 8 10 12

(a) Sample noise track signal con-taining transient events. Du-ration of 2.5 seconds.

2 4 6 8 10 12

(b)COE feature extracted from signal in figure 5.16a. d = 1

(c) COE feature extracted from signal in figure 5.16a. d= 512 samples.

(d)COE feature extracted from signal in figure 5.16a. d = 2048samples.

Figure 5.16: Noise track sample data containing transient events. COE fea-ture at differentdvalues.

To better understand the COE feature’s behaviour as used by theCOE detec-tor, the following figures can be used. Figure 5.16 shows how the COE feature behaves for different values ofd. The signal in figure 5.16a contains some tran-sient events in it. Figures 5.16b, 5.16c and 5.16d show how this feature changes as the parameter d increases. Recall that, according to the processing of the detector, the COE feature values obtained by window are normalized by its RMS value in that window. The general effect of extracting the COE feature is a concentration of the energy of the signal. This concentration is, recalling the COE theory, a summation of the energy in the past dsamples. However, if the value of dis high, an extreme concentration of the energy in the signal happens, making less evident the peaks of energy that characterize impulsive transient events. This is shown in figure 5.16d. Thus, there exists a parameterd that provides a good concentration of energy yielding better AU C(0.2)values.

In this case,d= 512samples produced the highestAU C(0.2)for this detector.

5.1 ROC results 73

Figure 5.17 shows the ROC curves for theCOEFREQdetector. In contrast with the TEO feature, the COE feature is suitable for its application in frequency bands.

(a)COEFREQ detector ROC, and detection strategy, d = 1sample.

(b)COEFREQ detector ROC, or detection strategy,d= 1 sample.

(c)COEFREQ detector ROC, and detection strategy, d = 512samples.

(d)COEFREQ detector ROC, or detection strategy, d = 512samples.

(e)COEFREQ detector ROC, and detection strategy,d = 2048samples.

(f )COEFREQ detector ROC, or detection strategy, d = 2048samples.

Figure 5.17: COEFREQ detector ROC curves.

The COE feature relies on the change of energy of the signal. Thus, a COE broadband analysis of a signal might not be able to detect tenuous changes of energy occurring in high frequency bands due to a masking effect by components

with more energy. Hence, the COE feature is suitable for a frequency band analysis.

This detector produces better results using theordetection strategy than when using the anddetection strategy. This can be observed in figures 5.17b, 5.17d and 5.17f. Recalling the or detection strategy, a window segment is declared as a positive when one or more COE feature values exceed a threshold in any frequency band. Thus, the detector is able to detect transient events even if the feature exceeds the threshold value in one frequency band.

The effect of varying parameter daffects the COEFREQ detector in the same way it affects theCOE detector, but in each frequency band. This is shown in figures 5.17b, 5.17d and 5.17f, whered= 512produced the bestAU C(0.2)for this detector.

Figure 5.18 shows the ROC curves for the LPS detector. As it can be seen from the figure, parameterST F T_window affects theAU C(0.2) values obtained.

However, in the STFT this parameter is related to the frequency resolution of the Fourier transform and to the time localization of any changes in frequency.

Thus, the change in AU C(0.2) is thought to be related to the duration of a transient event, where a window of the same length as an event would consider all of the energy injected by the event, producing high magnitude values in each frequency bin. Note how the bestAU C(0.2) values were achieved using a window of 512 samples for theCOE, COEFREQand LPS detectors.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(a) LPS detector ROC curve, with ST F Twindow = 512

(b)LPS detector ROC curve, with ST F Twindow = 2048 samples.

Figure 5.18: LPS detector ROC curves.