Iterative eigenvalue decomposition of Hankel matrix: An EMD like tool

Abstract

The decomposition of a multicomponent non-stationary signal is helpful in obtaining its time-frequency distribution (TFD). In this paper, a novel empirical mode decomposition (EMD)-like eigenvalue decomposition of Hankel matrix (EVDHM) technique is proposed, which extracts the mono-component signal using the sifting approach. In proposed method, two different eigenvalue threshold computation approaches are proposed: one is empirically defined and the other is based on minimum description length (MDL). In each iteration of EMD-like EVDHM method, EVDHM is performed on the signal and the significant elementary components (ECs) are obtained. Later, the most dominant mono-component signal is extracted from the obtained ECs using a new component grouping approach based on frequency spreads and instantaneous frequencies of the ECs and residue is considered as signal for next iteration. The separability conditions for the two sinusoidal multicomponent signals are studied for the proposed decomposition technique using the average correlation measure. Finally, the performance of the proposed method for signal decomposition is compared with empirical mode decomposition (EMD), ensemble EMD, variational mode decomposition, iterative filtering, Fourier decomposition method (FDM), empirical FDM, empirical wavelet transform (EWT), Fourier-Bessel series expansion-based EWT, singular spectral analysis, and improved EVDHM techniques for three clean and noisy synthetic signal and a real-world voiced speech signal. The proposed method is found to give the lowest error-to-signal ratio and the highest average correlation than the baselines for all the considered signals, with high-resolution TFD. Furthermore, the trend line extraction and weak component extraction have been performed using the proposed method. © 2025 Elsevier B.V., All rights reserved.