Stabilization and variations to the adaptive local iterative filtering algorithm: the fast resampled iterative filtering method

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Numerische Mathematik Pub Date : 2024-01-27 DOI:10.1007/s00211-024-01394-y

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引用次数: 0

Abstract

Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode Decomposition technique and the Iterative Filtering method. When a signal contains mono-components that have rapid varying instantaneous frequencies like chirps or whistles, it becomes particularly hard for most techniques to properly factor out these components. The Adaptive Local Iterative Filtering technique has recently gained interest in many applied fields of research for being able to deal with non-stationary signals presenting amplitude and frequency modulation. In this work, we address the open question of how to guarantee a priori convergence of this technique, and propose two new algorithms. The first method, called Stable Adaptive Local Iterative Filtering, is a stabilized version of the Adaptive Local Iterative Filtering that we prove to be always convergent. The stability, however, comes at the cost of higher complexity in the calculations. The second technique, called Resampled Iterative Filtering, is a new generalization of the Iterative Filtering method. We prove that Resampled Iterative Filtering is guaranteed to converge a priori for any kind of signal. Furthermore, we show that in the discrete setting its calculations can be drastically accelerated by leveraging on the mathematical properties of the matrices involved. Finally, we present some artificial and real-life examples to show the power and performance of the proposed methods.Kindly check and confirm that the Article note is correctly identified.

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自适应局部迭代滤波算法的稳定和变化：快速重采样迭代滤波法

摘要非稳态信号在现实生活中无处不在。在过去的几十年里，人们提出了许多技术，如开创性的经验模式分解技术和迭代滤波法，这些技术可以将多分量信号分解为简单的振荡单分量信号。当信号包含瞬时频率快速变化的单声道分量（如啁啾声或口哨声）时，大多数技术都很难正确地将这些分量剔除。最近，自适应局部迭代滤波技术在许多应用研究领域引起了人们的兴趣，因为它能够处理具有振幅和频率调制的非稳态信号。在这项工作中，我们解决了如何保证这种技术的先验收敛性这一未决问题，并提出了两种新算法。第一种方法称为稳定自适应局部迭代滤波法，是自适应局部迭代滤波法的稳定版本，我们证明它总是收敛的。然而，这种稳定性是以更高的计算复杂度为代价的。第二种技术称为重采样迭代滤波，是对迭代滤波方法的新概括。我们证明，对于任何类型的信号，重采样迭代滤波法都能保证先验收敛。此外，我们还证明，在离散环境中，利用相关矩阵的数学特性，可以大大加快计算速度。最后，我们列举了一些人工和现实生活中的例子，以展示所提方法的威力和性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerische Mathematik 数学-应用数学

CiteScore

4.10

自引率

4.80%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerische Mathematik publishes papers of the very highest quality presenting significantly new and important developments in all areas of Numerical Analysis. "Numerical Analysis" is here understood in its most general sense, as that part of Mathematics that covers: 1. The conception and mathematical analysis of efficient numerical schemes actually used on computers (the "core" of Numerical Analysis) 2. Optimization and Control Theory 3. Mathematical Modeling 4. The mathematical aspects of Scientific Computing