Iterative filtering as a direct method for the decomposition of nonstationary signals
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Iterative filtering as a direct method for the decomposition of nonstationary signals Antonio Cicone1,2,3 Received: 24 November 2018 / Accepted: 24 October 2019 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The Iterative Filtering method is a technique developed recently for the decomposition and analysis of nonstationary and nonlinear signals. In this work, we propose two alternative formulations of the original algorithm which allows to transform the iterative filtering method into a direct technique, making the algorithm closer to an online algorithm. We present a few numerical examples to show the effectiveness of the proposed approaches. Keywords Iterative filtering · Direct method · Signal decomposition · Nonstationary signal · Empirical mode decomposition · Fast algorithms · Fast Fourier transform · Nonlinear and nonstationary signals Mathematics Subject Classification (2010) 94A12 · 15A18 · 65F15 · 65T50
1 Introduction The iterative filtering (IF) method is, as the name suggests, an iterative algorithm proposed by Lin et al. in 2009 [27] as an alternative to the well known empirical mode decomposition (EMD) method. The EMD is part of the so-called Hilbert–Huang transform (HHT) technique [22] for the analysis of nonstationary and nonlinear signals. The aim of the EMD and IF is the decomposition of a given signal into simple components, defined by Huang [22] as intrinsic mode functions (IMFs), which are oscillatory functions that fulfills two empirical properties: the two curves connecting Antonio Cicone
[email protected] 1
Istituto Nazionale di Alta Matematica, P.le Aldo Moro 5, 00185, Roma, Italy
2
DISIM, Universit`a degli Studi dell’Aquila, via Vetoio n.1, 67100, L’Aquila, Italy
3
Gran Sasso Science Institute, Via Michele Jacobucci, 2, 67100 L’Aquila, Italy
Numerical Algorithms
respectively the maxima and minima of an IMF have to be symmetric with respect to the horizontal line; the number of zero crossing must equal plus or minus one the number of local extrema of an IMF [5]. Once a nonstationary and nonlinear signal has been decomposed into IMFs with different scales, it is possible to study its properties to unravel potentially hidden features. Furthermore, such decomposition allows for a more accurate time-frequency analysis of the signal itself. The EMD and IF decomposition methods have been applied to the study of a wide variety of datasets. For instance, in Medicine, they have been used for the automatic identification of seizure-free electroencephalographic signals [33], for the study of the gastroesophageal reflux disease [26], for the derivation of the respiratory sinus arrhythmia from the heartbeat time series [1], for the analysis of the heart rate variability [15], to denoise the electrocardiographic signal and correct the baseline wander [3], to study the dengue virus spread [20], for the identification of the coupling between prefrontal and visual cortex [18], to sense the instantaneous heart rate and instantaneous respiratory rate from pho
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