{"data":{"id":"10.6084/m9.figshare.c.3716299.v1","type":"dois","attributes":{"doi":"10.6084/m9.figshare.c.3716299.v1","prefix":"10.6084","suffix":"m9.figshare.c.3716299.v1","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"},{"relationType":"IsIdenticalTo","relatedIdentifier":"10.6084/m9.figshare.c.3716299","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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","url":"https://figshare.com/collections/Supplementary_material_from_The_Fourier_decomposition_method_for_nonlinear_and_non-stationary_time_series_analysis_/3716299/1","contentUrl":null,"metadataVersion":2,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":1,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2017-03-14T10:03:45.000Z","registered":"2017-03-14T10:03:46.000Z","published":"2017","updated":"2024-12-19T09:50:14.000Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}},"provider":{"data":{"id":"otjm","type":"providers"}},"media":{"data":{"id":"10.6084/m9.figshare.c.3716299.v1","type":"media"}},"references":{"data":[{"id":"10.1098/rspa.2016.0871","type":"dois"}]},"citations":{"data":[]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[]}}}}