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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:373

Article; Proceedings Paper

Cicone, Antonio^1,2,3  Dell'Acqua, Pietro⁴ 

[1] Ist Nazl Alta Matemat, Ple Aldo Moro 5, I-00185 Rome, Italy

[2] Univ Aquila, DISIM, Via Vetoio 1, I-67100 Laquila, Italy

[3] Gran Sasso Sci Inst, Viale Francesco Crispi 7, I-67100 Laquila, Italy

[4] Libera Univ Bolzano, Piazza Domenicani 3, I-39100 Bolzano, Italy

关键词: Signal decomposition;    Boundary conditions;    Structured matrices;    Iterative filtering;    Empirical mode decomposition;    Nonstationary signal;   

DOI  :  10.1016/j.cam.2019.04.028

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free