Stabilization and Variations to the Adaptive Local Iterative Filtering Algorithm: the Fast Resampled Iterative Filtering Method
Giovanni Barbarino, Antonio Cicone
TL;DR
The paper tackles the challenge of decomposing non-stationary signals with rapidly changing instantaneous frequencies by extending IF/ALIF with two convergent, flexible frameworks. It introduces Stable ALIF (SALIF) with guaranteed convergence and Resampled Iterative Filtering (RIF), plus Fast Resampled Iterative Filtering (FRIF) for FFT-accelerated computation in the discrete setting. The authors prove a priori convergence for SALIF and for RIF/FRIF, and demonstrate through synthetic and real data that FRIF achieves accurate IMF extraction with substantially reduced runtimes compared to ALIF and SALIF. This work broadens the applicability of adaptive local filtering to chirp-like components and enables scalable analysis via FFT-based implementations.
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, 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.