Structural break estimation of noisy sinusoidal signals

In this article we consider the problem of partitioning a signal sequence into a set of signal sub-sequences, in such a way that each sub-sequence can be adequately modeled by a superposition of different sinusoids. In our formulation, the number of sub-sequences, the points at which two adjacent sub-sequences join, as well as the sinusoid composition in each sub-sequence are assumed unknown. We recast this problem as a statistical model selection problem, and invoke the minimum description length principle to construct estimators for these unknowns. As to be shown, these estimators are defined as the joint optimizer of a relatively complex objective function, and a genetic algorithm is developed for solving the corresponding optimization problem. The empirical performance of the resulting partitioning procedure is evaluated by a set of numerical experiments. The procedure is also applied to aid solving a classification problem that involves earthquake and explosion data.