Adaptive Bandwidth Fourier Decomposition Method for Multi-Component Signal Processing

Variational mode decomposition (VMD) is a practical signal decomposition approach, which extracts the modes through bandwidth optimization in the frequency domain. In recent years, many efforts have been made to attenuate the effect of prior parameters, which heavily trouble the traditional VMD. However, as the core step, the bandwidth optimization algorithm including the initialization of center frequencies in VMD is rarely discussed or improved in the existing work. In practical applications, the non-convergence or unreasonable convergence of the bandwidth optimization can lead to the failure of VMD in mode separation. Thus, in this paper, a new signal decomposition method termed adaptive bandwidth Fourier decomposition (ABFD) is proposed to separate the narrowband components from a complicated signal accurately. The proposed ABFD inherits the idea of implementing Fourier spectrum decomposition through bandwidth optimization. In particular, three significant improvements are made in this work. Firstly, in order to reduce the computation complexity, a novel bandwidth optimization algorithm termed Fourier spectrum bandwidth optimization (FSBO) is proposed. Secondly, inspired by the empirical principle proposed in the empirical wavelet transform (EWT), a novel variable initialization method based on spectral energy distribution is introduced. Finally, under the guidance of narrowband characteristics, a method for automatically detecting the appropriate mode number is developed. In order to evaluate the performance of the proposed ABFD, simulation analysis and measured signal analysis are carried out in this paper. The preliminary results indicate that the proposed ABFD can extract the single components more accurately than EMD and VMD.