TR32-Database: Database of Transregio 32

[741] - Fast empirical mode decompositions of multivariate data based on adaptive spline-wavelets and a generalization of the Hilbert-Huang-transform (HHT) to arbitrary space dimensions

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Citation
Jager, G., Koch, R., Kunoth, A., Pabel, R., 2010. Fast empirical mode decompositions of multivariate data based on adaptive spline-wavelets and a generalization of the Hilbert-Huang-transform (HHT) to arbitrary space dimensions. Advances in Adaptive Data Analysis (AADA), 2 (3), 337 - 358. DOI: 10.1142/S1793536910000513.
Identification
Title(s):Main Title: Fast empirical mode decompositions of multivariate data based on adaptive spline-wavelets and a generalization of the Hilbert-Huang-transform (HHT) to arbitrary space dimensions
Description(s):Abstract: The Hilbert-Huang-Transform (HHT) has proven to be an appropriate multiscale analysis technique specifically for nonlinear and nonstationary time series on non-equidistant grids. It is empirically adapted to the data: first, an additive decomposition of the data (empirical mode decomposition, EMD) into certain multiscale components is computed, denoted as intrinsic mode functions. Second, to each of these components, the Hilbert transform is applied. The resulting Hilbert spectrum of the modes provides a localized time-frequency spectrum and instantaneous (time-dependent) frequencies. For the first step, the empirical decomposition of the data, a different method based on local means has been developed by Chen et al. (2006). In this paper, we extend their method to multivariate data sets in arbitrary space dimensions. We place special emphasis on deriving a method which is numerically fast also in higher dimensions. Our method works in a coarse-to-fine fashion and is based on adaptive (tensor-product) spline-wavelets. We provide some numerical comparisons to a method based on linear infinite elements and one based on thin-plate-splines to demonstrate the performance of our method, both with respect to the quality of the approximation as well as the numerical efficiency. Second, for a generalization of the Hilbert transform to the multivariate case, we consider the Riesz transformation and an embedding into Clifford-algebra valued functions, from which instantaneous amplitudes, phases and orientations can be derived. We conclude with some numerical examples.
Identifier(s):DOI: 10.1142/S1793536910000513
Responsible Party
Creator(s):Author: Gabriela Jager
Author: Robin Koch
Author: Angela Kunoth
Author: Roland Pabel
Publisher:World Scienti c Publishing Company
Topic
TR32 Topic:Other
Related Sub-project(s):C1, C7
Subject(s):CRC/TR32 Keywords: Multivariate Data Analysis, HHT, Tensor Product Spline Wavelets, Wavelet, Monogenic Function, Clifford Algebra, Riesz Transform
File Details
File Name:2010_Jager_AADA.pdf
Data Type:Text
Size(s):22 Pages
File Size:3184 kB (3.109 MB)
Date(s):Issued: 2010-07-01
Mime Type:application/pdf
Data Format:PDF
Language:English
Status:Completed
Constraints
Download Permission:OnlyTR32
General Access and Use Conditions:For internal use only
Access Limitations:For internal use only
Licence:TR32DB Data policy agreement
Geographic
North:-no map data
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Measurement Region:Other
Measurement Location:--Other--
Specific Informations - Publication
Status:Published
Review:PeerReview
Year:2010
Type:Article
Article Type:Journal
Source:Advances in Adaptive Data Analysis (AADA)
Issue:3
Volume:2
Number Of Pages:22
Page Range:337 - 358
Metadata Details
Metadata Creator:Roland Pabel
Metadata Created:2013-12-02
Metadata Last Updated:2013-12-02
Subproject:C1
Funding Phase:1
Metadata Language:English
Metadata Version:V40
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Metadata Downloads:0
Dataset Downloads:1
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