Empirical Fourier Decomposition: An Accurate Adaptive Signal Decomposition Method

TL;DR

The paper introduces the empirical Fourier decomposition (EFD), an adaptive signal decomposition method that improves accuracy, consistency, and efficiency over existing techniques like EWT and FDM, especially for complex non-stationary signals.

Contribution

The paper proposes the EFD, combining an improved Fourier spectrum segmentation and an ideal filter bank, to address mode mixing and inconsistency issues in signal decomposition.

Findings

EFD provides accurate and consistent decomposition for complex signals.

EFD outperforms EWT, FDM, VMD, and EMD in accuracy and efficiency.

EFD yields superior time-frequency representations.

Abstract

Signal decomposition is an effective tool to assist the identification of modal information in time-domain signals. Two signal decomposition methods, including the empirical wavelet transform (EWT) and Fourier decomposition method (FDM), have been developed based on Fourier theory. However, the EWT can suffer from a mode mixing problem for signals with closely-spaced modes and decomposition results by FDM can suffer from an inconsistency problem. An accurate adaptive signal decomposition method, called the empirical Fourier decomposition (EFD), is proposed to solve the problems in this work. The proposed EFD combines the uses of an improved Fourier spectrum segmentation technique and an ideal filter bank. The segmentation technique can solve the inconsistency problem by predefining the number of modes in a signal to be decomposed and filter functions in the ideal filter bank have no transition phases, which can solve the mode mixing problem. Numerical investigations are conducted to study the accuracy of the EFD. It is shown that the EFD can yield accurate and consistent decomposition results for signals with multiple non-stationary modes and those with closely-spaced modes, compared with decomposition results by the EWT, FDM, variational mode decomposition and empirical mode decomposition. It is also shown that the EFD can yield accurate time-frequency representation results and it has the highest computational efficiency among the compared methods.