Data · collection · 2017
Supplementary material from "The Fourier decomposition method for nonlinear and non-stationary time series analysis"
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For many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data.
Description
In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs).
The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM.
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The proposed MFDM generates a finite number of bandlimited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time–frequency–energy (TFE) distribution that reveals the intrinsic structure of a data.
Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.
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- Repository landing page figshare.com/collections/Supplementary_material_from_The_Fourier_decomposit… ↗
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- DOI doi.org/10.6084/m9.figshare.c.3716299.v1 ↗
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- CC BY creativecommons.org/licenses/by/4.0 ↗
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- IsSupplementTo 10.1098/rspa.2016.0871 doi.org/10.1098/rspa.2016.0871 ↗
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Topics
- Stated by source
- Computer and information sciences · Electrical engineering, electronic engineering, information engineering
- Inferred from text
- Communications engineering 75%
Related
Provenance · 1 source records, 10 field assertions
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| DataCite | 10.6084/m9.figshare.c.3716299.v1 | 14 d ago | JSON v1 |
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