  In this paper, a novel decomposition method for non-stationary and nonlinear
signals is proposed. This method is inspired by the adaptive wavelet filter
bank of the empirical wavelet transform (EWT) and Fourier intrinsic band
functions (FIBFs) of the Fourier decomposition method (FDM). Therefore, the
proposed approach is entitled as empirical Fourier decomposition (EFD). EFD is
defined as the adaptive bandpass filter bank, regarded as the adaptive FIBFs
based on the segment of the Fourier spectrum. Firstly, an enhanced segmentation
technology of the Fourier spectrum based is presented. Secondly, the framework
of EFD is established both in a continuous series and a discrete series.
Finally, combined with the Hilbert transform, EFD is extended to a
time-frequency representation. To verify the effectiveness of EFD, three
non-stationary multimode signals, a simulated free vibration, and one real ECG
signal are tested. The results manifest that EFD is more effective, compared
with EWT and FDM, with higher processing precision, computation efficiency and
noise robustness particularly to the closely-spaced frequencies and
high-frequency noise.
