Structural Break Estimation of Noisy Sinusoidal Signals

Signal Processing, 90(1), 303–312
R. K. W. Wong, R. C. S. Lai and T. C. M. Lee

Abstract

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.