The use of wavelet packets for event detection

In this paper, we propose a best basis selection method to choose a set of packets from a wavelet packet tree. Our goal is to obtain packets that show changes in both energy and frequency. The criterion adapted to choose the best basis is the Kullback-Leibler Distance (KLD). When there is no event to be detected, the estimated KLD follows roughly an exponential distribution depending on only one parameter: the length of the windows partitioning the signal. When events are detected in a packet, the distribution of the estimated KLD deviates from the exponential distribution. The statistics Kolmogorov-Smirnov are used to measure the separation between experimental and theoretical cumulative distributions in order to highlight the presence of ruptures, then to select the most relevant packets.