Conjectures on spectral properties of ALIF algorithm

Giovanni Barbarino, Antonio Cicone*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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 [9], 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 [9], and in doing so, we also develop new theory and results for the GLT sequences.

Original languageEnglish
Pages (from-to)127-152
Number of pages26
JournalLinear Algebra and Its Applications
Volume647
DOIs
Publication statusPublished - 15 Aug 2022
MoE publication typeA1 Journal article-refereed

Keywords

  • Adaptive local iterative filtering
  • Convergence analysis
  • Eigenvalue distribution
  • Empirical mode decomposition
  • Generalized locally Toeplitz sequences
  • Iterative filtering
  • Nonostationary signals
  • Signal decomposition

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