A new decomposition method for nonstationary signals, named Adaptive Local Iterative Filtering (ALIF), has been recently proposed in the literature. Given its similarity with the Empirical Mode Decomposition (EMD) and its more rigorous mathematical structure, which makes feasible to study its convergence compared to EMD, ALIF has really good potentiality to become a reference method in the analysis of signals containing strong nonstationary components, like chirps, multipaths and whistles, in many applications, like Physics, Engineering, Medicine and Finance, to name a few. In [11], the authors analyzed the spectral properties of the matrices produced by the ALIF method, in order to study its stability. Various results are achieved in that work through the use of Generalized Locally Toeplitz (GLT) sequences theory, a powerful tool originally designed to extract information on the asymptotic behavior of the spectra for PDE discretization matrices. In this manuscript we focus on answering some of the open questions contained in [11], and in doing so, we also develop new theory and results for the GLT sequences.

翻译：文献中最近提出了非静止信号的新的分解方法,名为适应性局部迭代过滤法(ALIF),在文献中最近提出了一个新的非静止信号分解法(ALIF),鉴于它与实验模式分解法(EMD)及其更为严格的数学结构相似,因此可以研究其与EMD的趋同性,ALIF在分析含有强大的非静止组成部分的信号(如焦耳、多路径和哨子)的信号方面确实具有极大的潜力,例如在物理、工程、医药和金融等许多应用中。在[11]中,作者分析了ALIF方法产生的矩阵的光谱特性,以便研究其稳定性。通过使用通用的Tolict(GLT)序列理论(GLT)在这项工作中取得了各种成果,该理论最初设计为PDE离散式矩阵的光谱系无症状行为提取信息的有力工具。在这个手稿中,我们集中回答在[11]中所包含的一些开放问题,并在这样做时,我们还为GLT序列开发新的理论和结果。