Theoretical Framework for A Succinct Empirical Mode Decomposition

Journal article (2023)

Authors

J. Jin Railway Engineering - CEG
Z. Li Railway Engineering - CEG
Research Group
Railway Engineering (CEG) (TU Delft)
Copyright: © 2023 J. Jin, Z. Li
DOI: https://doi.org/10.1109/LSP.2023.3293468
Interpolation Time-frequency analysis Time-varying filters Filter banks Eigenvalues and eigenfunctions Time-frequency analysis Adaptive signal processing Empirical mode decomposition Filtering theory Low-pass filters Splines (mathematics)
More Info
expand_more

Published Date

2023

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Civil Engineering & Geosciences

Department

Engineering Structures

Research Group

Railway Engineering

Abstract

Empirical mode decomposition (EMD) lacks a strong theoretical support although extensively applied. We propose a theoretical framework for a succinct EMD in this work, with the assumption of invariant extrema locations for one IMF extraction. We define the envelope mean filter (EMF) and prove that the filter matrix satisfies five properties. The sifting matrix is convergent to an idempotent matrix. An IMF is the projection of the input signal on the generalized eigenspace of the EMF matrix. An IMF is orthogonal to the residual signal, but different IMFs have no orthogonality. With numerical experiments on different signals, our framework achieves similar results to the classic EMD.