Convergence analysis of Adaptive Locally Iterative Filtering and SIFT method

TL;DR

This paper provides the first convergence analysis of Adaptive Local Iterative Filtering (ALIF) and introduces SIFT, a robust method combining synchrosqueezing with ALIF for decomposing highly nonstationary signals.

Contribution

It offers a convergence proof for ALIF and proposes SIFT, a novel adaptive decomposition technique for noisy, nonstationary signals.

Findings

ALIF convergence is established for complex signals.

SIFT effectively decomposes highly nonstationary signals.

Numerical results demonstrate SIFT's robustness and accuracy.

Abstract

Adaptive Local Iterative Filtering (ALIF) is a currently proposed novel time-frequency analysis tool. It has been empirically shown that ALIF is able to separate components and overcome the mode-mixing problem. However, so far its convergence is still an open problem, particularly for highly nonstationary signals, due to the fact that the kernel associated with ALIF is non-translational invariant, non-convolutional and non-symmetric. Our first contribution in this work is providing a convergence analysis of ALIF. From the practical perspective, ALIF depends on a robust frequencies estimator, based on which the decomposition can be achieved. Our second contribution is proposing a robust and adaptive decomposition method for noisy and nonstationary signals, which we coined the Synchrosqueezing Iterative Filtering Technique (SIFT). In SIFT, we apply the synchrosqueezing transform to estimate the instantaneous frequency, and then apply the ALIF to decompose a signal. We show numerically the ability of this new approach in handling highly nonstationary signals.