{"data":{"id":"10.6084/m9.figshare.c.3716299","type":"dois","attributes":{"doi":"10.6084/m9.figshare.c.3716299","prefix":"10.6084","suffix":"m9.figshare.c.3716299","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Pushpendra Singh","affiliation":[],"nameIdentifiers":[]},{"name":"Joshi, Shiv Dutt","nameType":"Personal","givenName":"Shiv Dutt","familyName":"Joshi","affiliation":[],"nameIdentifiers":[]},{"name":"Patney, Rakesh Kumar","nameType":"Personal","givenName":"Rakesh Kumar","familyName":"Patney","affiliation":[],"nameIdentifiers":[]},{"name":"Saha, Kaushik","nameType":"Personal","givenName":"Kaushik","familyName":"Saha","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Supplementary material from \"The Fourier decomposition method for nonlinear and non-stationary time series analysis\""}],"publisher":"Figshare","container":{},"publicationYear":2017,"subjects":[{"subject":"90699 Electrical and Electronic Engineering not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Electrical engineering, electronic engineering, information engineering","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"80110 Simulation and Modelling","subjectScheme":"FOR"},{"subject":"FOS: Computer and information sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"80401 Coding and Information Theory","subjectScheme":"FOR"}],"contributors":[],"dates":[{"date":"2017-03-14","dateType":"Created"},{"date":"2017-03-14","dateType":"Updated"},{"date":"2017","dateType":"Issued"}],"language":null,"types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"Collection","resourceType":"Collection","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1098/rspa.2016.0871","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rights":"CC BY","rightsUri":"https://creativecommons.org/licenses/by/4.0"}],"descriptions":[{"description":"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. 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. 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.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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