经验傅里叶分解：一种精确的自适应信号分解方法
Empirical Fourier Decomposition: An Accurate Adaptive Signal Decomposition Method
摘要：
信号分解是辅助识别时域信号模态信息的有效工具。基于傅立叶变换理论，提出了两种信号分解方法：经验小波变换（EWT）和傅立叶分解法（FDM）。然而，EWT可能遭受模式混合问题的信号与密集模式和FDM的分解结果可能遭受不一致的问题。提出了一种精确的自适应信号分解方法，称为经验傅里叶分解（EFD），以解决这项工作中的问题。建议EFD结合使用改进的傅立叶频谱分割技术和理想的滤波器组。分割技术通过预先定义待分解信号中的模式数来解决不一致性问题，并且理想滤波器组中的滤波器函数没有过渡相位，这可以解决模式混合问题。数值研究进行了研究的EFD的精度。结果表明，与EWT、FDM、变分模式分解和经验模式分解的结果相比，EFD对多个非平稳模式和密集模式信号的分解结果准确一致。研究结果还表明，EFD可以得到准确的时频表示结果，并且在比较的方法中具有最高的计算效率。
英文摘要：
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.
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