非平稳信号分析的广义解析模态分解方法

现有的非平稳信号分析方法都有各自不同的缺陷，短时傅里叶变换的时频分辨率受不确定性原理的限制，希尔伯特黄变换存在端点效应和模态混叠，易导致模糊的时频分布；解析模态分解只适合分析频率恒定的多分量信号；针对包含多个时变模态、特别是频谱重叠的非平稳信号，本文提出了一种新的信号分析方法———广义解析模态分解（Generalized Analytical Mode Decomposition，GAMD）．GAMD通过广义傅里叶变换将时变频率转换为频谱可分的，采用解析模态分解对其分解，再对得到的单分量信号进行逆广义傅里叶变换即可得到原始信号的分量．因此，GAMD非常适合分析时变的非平稳信号．通过仿真信号将GAMD与短时傅里叶变换和希尔伯特黄变换等方法进行了对比，结果表明GAMD方法的分解效果更精确，时频分辨率更高．

GeneraIized AnaIyticaI Mode Deco mposition for Non-Stationary SignaI AnaIysis

The existing methods for analyzing non-stationary signal all have different defects.The time-frequency res-olution of short-time Fourier transform is limited by the uncertainty principle.The boundary effect and mode mixing of Hil-bert-Huang transform often result in an unclear time-frequency distribution.Analytical mode decomposition is only suitable for analyzing multi-component signal with constant frequencies.For the multi-component signal with time-varying frequen-cies,especially when the spectrum overlaps,a method termed generalized analytical mode decomposition (GAMD)is pro-posed for analyzing these signals.In GAMD,generalized Fourier transform is used to convert the time-varying frequencies to constant ones without overlapping in spectrum and then the analytical mode decomposition is adopted to handle the trans-formed signal.Lastly,the inverse generalized Fourier transform is used to demodulate the obtained mono-components. Hence,GAMD is very suitable for analyzing time-varying non-stationary signals.The proposed GAMD method is compared with short-time Fourier transform and Hilbert-Huang transform through analyzing simulation signals and the results indicate that GAMD possesses more accurate decomposing results and higher time-frequency resolution.