Divergence-Based Segmentation Algorithm for Heavy-Tailed Acoustic Signals with Time-Varying Characteristics

Many real-world systems change their parameters during the operation. Thus, before the analysis of the data, there is a need to divide the raw signal into parts that can be considered as homogeneous segments. In this paper, we propose a segmentation procedure that can be applied for the signal with time-varying characteristics. Moreover, we assume that the examined signal exhibits impulsive behavior, thus it corresponds to the so-called heavy-tailed class of distributions. Due to the specific behavior of the data, classical algorithms known from the literature cannot be used directly in the segmentation procedure. In the considered case, the transition between parts corresponding to homogeneous segments is smooth and non-linear. This causes that the segmentation algorithm is more complex than in the classical case. We propose to apply the divergence measures that are based on the distance between the probability density functions for the two examined distributions. The novel segmentation algorithm is applied to real acoustic signals acquired during coffee grinding. Justification of the methodology has been performed experimentally and using Monte-Carlo simulations for data from the model with heavy-tailed distribution (here the stable distribution) with time-varying parameters. Although the methodology is demonstrated for a specific case, it can be extended to any process with time-changing characteristics.