But each filter bank cuts the number of points, and hence the time resolution, by 2. FFTs, on the other hand, lose all time information. Because the warning signal is unique, the transforms produce a significant coefficient only when the warning signal appears. The computers detect the presence of the large coefficient and trigger alarms. You can do more with wavelets than just use them to analyze portions of a waveform.
Wavelets are also useful in data compression and other forms of signal processing.
Once you've transformed a time-domain signal into the wavelet domain, you can process the signal and perform an inverse wavelet transform to reconstruct the signal. The top plot in Figure 5 shows an EKG signal. The second plot shows the output after one stage of high-pass filtering. By performing some calculations, you can reconstruct a signal minus any unwanted components. An application of this is in the removal of noise.