Study of boundary conditions in the Iterative Filtering method for the decomposition of nonstationary signals

Abstract

Nonstationary and non-linear signals are ubiquitous in real life. Their decomposition and analysis is an important research topic of signal processing. Recently a new technique, called Iterative Filtering, has been developed with the goal of decomposing such signals into simple oscillatory components. Several papers have been devoted to the investigation of this technique from a mathematical point of view. All these works start with the assumption that each compactly supported signal is extended periodically outside the boundaries. In this work, we tackle the problem of studying the influence of different boundary conditions on the decompositions produced by the Iterative Filtering method. In particular, the choice of boundary conditions gives rise to different types of structured matrices. Thus, we describe their spectral properties and the convergence properties of Iterative Filtering algorithm when such matrices are involved. Numerical results on artificial and real life signals provide interesting insight on important aspects such as accuracy and error propagation of the proposed technique and pave the way for further promising developments.