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.

中文翻译：

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自适应局部迭代滤波算法的稳定性和变化：快速重采样迭代滤波方法

摘要

非平稳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，可以将多分量信号分解为简单的振荡单分量信号，例如突破性的经验模式分解技术和迭代滤波方法。当信号包含具有快速变化的瞬时频率（如线性调频声或口哨声）的单分量时，大多数技术很难正确地分解这些分量。自适应局部迭代滤波技术最近在许多应用研究领域引起了人们的兴趣，因为它能够处理呈现幅度和频率调制的非平稳信号。在这项工作中，我们解决了如何保证该技术的先验收敛的悬而未决的问题，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过滤，是自适应局部迭代过滤的稳定版本，我们证明它总是收敛的。然而，稳定性是以更高的计算复杂性为代价的。第二种技术称为重采样迭代过滤，是迭代过滤方法的新推广。我们证明重采样迭代滤波对于任何类型的信号都保证先验收敛。此外，我们表明，在离散设置中，通过利用所涉及矩阵的数学特性可以大大加速其计算。最后，我们提供了一些人工和现实例子来展示所提出方法的威力和性能。请检查并确认文章注释已正确识别。