Theoretical Framework for A Succinct Empirical Mode Decomposition

Yang Jin; Zili Li

doi:10.1109/LSP.2023.3293468

Theoretical Framework for A Succinct Empirical Mode Decomposition

Yang Jin, Zili Li

Railway Engineering

Research output: Contribution to journal › Article › Scientific › peer-review

5 Downloads (Pure)

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.

Original language	English
Pages (from-to)	888-892
Number of pages	5
Journal	IEEE Signal Processing Letters
Volume	30
DOIs	https://doi.org/10.1109/LSP.2023.3293468
Publication status	Published - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

adaptive signal processing
Eigenvalues and eigenfunctions
Empirical mode decomposition
Filter banks
Filtering theory
Interpolation
Low-pass filters
Splines (mathematics)
time-frequency analysis
Time-frequency analysis
time-varying filters

Access to Document

10.1109/LSP.2023.3293468

Theoretical Framework for A Succinct Empirical Mode DecompositionFinal published version, 757 KB

Cite this

@article{089074d0eb9b41378cb06fc23f99c2f0,

title = "Theoretical Framework for A Succinct Empirical Mode Decomposition",

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.",

keywords = "adaptive signal processing, Eigenvalues and eigenfunctions, Empirical mode decomposition, Filter banks, Filtering theory, Interpolation, Low-pass filters, Splines (mathematics), time-frequency analysis, Time-frequency analysis, time-varying filters",

author = "Yang Jin and Zili Li",

note = "Green Open Access added to TU Delft Institutional Repository {\textquoteleft}You share, we take care!{\textquoteright} – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. ",

year = "2023",

doi = "10.1109/LSP.2023.3293468",

language = "English",

volume = "30",

pages = "888--892",

journal = "IEEE Signal Processing Letters",

issn = "1070-9908",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

}

TY - JOUR

T1 - Theoretical Framework for A Succinct Empirical Mode Decomposition

AU - Jin, Yang

AU - Li, Zili

N1 - Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - adaptive signal processing

KW - Eigenvalues and eigenfunctions

KW - Empirical mode decomposition

KW - Filter banks

KW - Filtering theory

KW - Interpolation

KW - Low-pass filters

KW - Splines (mathematics)

KW - time-frequency analysis

KW - Time-frequency analysis

KW - time-varying filters

UR - http://www.scopus.com/inward/record.url?scp=85164427421&partnerID=8YFLogxK

U2 - 10.1109/LSP.2023.3293468

DO - 10.1109/LSP.2023.3293468

M3 - Article

AN - SCOPUS:85164427421

SN - 1070-9908

VL - 30

SP - 888

EP - 892

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

ER -

Theoretical Framework for A Succinct Empirical Mode Decomposition

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this