论文标题
关于Alif算法光谱特性的猜想
Conjectures on spectral properties of ALIF algorithm
论文作者
论文摘要
最近在文献中提出了一种新的非组织信号分解方法，称为自适应局部迭代过滤（ALIF）。鉴于它与经验模式分解（EMD）及其更严格的数学结构相似，这使得与EMD相比，研究其融合可行，Alif在分析包含强大的非机构组件的信号的参考方法中确实具有良好的潜力，例如Chirps，Multiperths和Whistles，例如在许多应用程序中，在许多应用程序中，例如物理学，工具，工具，名称，名称，均等。 在[11]中，作者分析了Alif方法产生的矩阵的光谱特性，以研究其稳定性。通过使用广义的局部toeplitz（GLT）序列理论，这项工作实现了各种结果，这是一种强大的工具，该工具最初旨在提取有关PDE离散化矩阵的光谱的渐近行为的信息。在本手稿中，我们专注于回答[11]中包含的一些开放问题，并为此，我们还为GLT序列开发了新的理论和结果。
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.
