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, we can think, for instance, to 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, in the discrete setting, by leveraging on the mathematical properties of the matrices involved, we show that its calculations can be accelerated drastically. Finally, we present some artificial and real-life examples to show the powerfulness and performance of the proposed methods.

翻译：非平稳信号在现实生活中普遍存在。近几十年来，已有多种技术被提出，能够将多分量信号分解为简单的振荡单分量，例如开创性的经验模态分解技术和迭代滤波方法。当信号中包含具有快速变化瞬时频率的单分量（例如线性调频或啁啾信号）时，大多数技术难以正确分离这些分量。自适应局部迭代滤波技术因其能够处理具有幅度和频率调制的非平稳信号，近年来在众多应用研究领域引起关注。本研究针对如何先验保证该技术收敛性的开放性问题，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，是自适应局部迭代滤波的稳定化版本，我们证明其总是收敛的。然而，稳定性是以计算复杂度的增加为代价的。第二种技术称为重采样迭代滤波，是迭代滤波方法的新泛化形式。我们证明，对于任何类型的信号，重采样迭代滤波都能先验保证收敛。此外，在离散设定下，通过利用所涉及矩阵的数学性质，我们表明其计算速度可以大幅提升。最后，我们通过人工和真实案例展示了所提方法的强大性能。