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Numerical analysis for iterative filtering with new efficient implementations based on FFT

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Abstract

The development of methods able to extract hidden features from non-stationary and non-linear signals in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem of further analyzing the convergence of the Iterative Filtering method both in a continuous and a discrete setting in order to provide a comprehensive analysis of its behavior. Based on these results we provide a new efficient implementation of Iterative Filtering algorithm, called Fast Iterative Filtering, which reduces the original iterative algorithm computational complexity by utilizing, in a nontrivial way, Fast Fourier Transform in the computations.

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Notes

  1. The original work by Huang et al. [41] as received so far, by itself, more than 14600 unique citations, according to Scopus.

  2. www.cicone.com.

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Acknowledgements

This work was supported by NSF Awards DMS-1620345, DMS-1830225, ONR Award N00014-18-1-2852, the Istituto Nazionale di Alta Matematica (INdAM) “INdAM Fellowships in Mathematics and/or Applications cofunded by Marie Curie Actions”, FP7-PEOPLE-2012-COFUND, Grant agreement n. PCOFUND-GA-2012-600198, the “Progetto Premiale FOE 2014” “Strategic Initiatives for the Environment and Security - SIES” of the INdAM and the CSES-Limadou project of the Istituto di Astrofisica e Planetologia Spaziali (IAPS) of the Istituto Nazionale di Astrofisica (INAF). Antonio Cicone is a member of the Italian “Gruppo Nazionale di Calcolo Scientifico” (GNCS) of the Istituto Nazionale di Alta Matematica “Francesco Severi” (INdAM). The authors thanks Giovanni Barbarino and Leonardo Robol for the interesting discussions they had on this topic.

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  1. DISIM, Università degli Studi dell’Aquila, Via Vetoio n. 1, 67100, L’Aquila, Italy

    Antonio Cicone

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Haomin Zhou

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Cicone, A., Zhou, H. Numerical analysis for iterative filtering with new efficient implementations based on FFT. Numer. Math. 147, 1–28 (2021). https://doi.org/10.1007/s00211-020-01165-5

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