Theoretical Framework for A Succinct Empirical Mode Decomposition

Theoretical Framework for A Succinct Empirical Mode Decomposition

Jin, J. (TU Delft Railway Engineering)
Li, Z. (TU Delft Railway Engineering)

2023

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.

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

http://resolver.tudelft.nl/uuid:089074d0-eb9b-4137-8cb0-6fc23f99c2f0

https://doi.org/10.1109/LSP.2023.3293468

2024-01-07

1070-9908

IEEE Signal Processing Letters, 30, 888-892

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.

Institutional Repository

journal article

© 2023 J. Jin, Z. Li