Empirical Fourier decomposition: An accurate signal decomposition method for nonlinear and non-stationary time series analysis

Signal decomposition is an effective tool to assist identification of modal information in timedomain 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 from a trivial component problem resulting in a trivial residual in the first decomposed component. Decomposition results by FDM can suffer from an inconsistency problem. In this work, an accurate adaptive signal decomposition method, called the empirical Fourier decomposition (EFD), is proposed to solve the aforementioned problems. The proposed EFD combines the uses of an improved Fourier spectrum segmentation technique and a zero-phase filter bank. The segmentation technique solves the trivial component problem by an adaptive sorting process and the inconsistency problem by predefining the number of components in a signal to be decomposed. The zero-phase filter bank has no transition phases, which exist in the EWT, in its each filter function, and it can solve the mode mixing problem. Numerical investigations are conducted to study the effectiveness and 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 decomposition methods. An experimental validation is also conducted to study the effectiveness of the EFD for experimentally measured signals with closelyspaced modes. It is shown that the EFD can decompose a signal with closely-spaced modes with higher accuracy, compared with the other decomposition methods.