基于递归希尔伯特变换的振动信号解调和瞬时频率计算方法

精确地提取振动信号的瞬时幅值和瞬时频率对结构的参数识别和健康监测有重要作用。希尔伯特变换是一种常用的信号解调及瞬时频率计算方法，但在信号不满足Bedrosian乘积定理的条件时会造成较大误差。针对这一问题，提出了一种递归希尔伯特变换方法，用前一步希尔伯特变换计算出的纯调频信号作为新的信号，递归地使用希尔伯特变换以进行信号解调，理论分析表明递归希尔伯特变换能够快速地收敛。最后采用仿真信号对比了递归希尔伯特变换与单次希尔伯特变换、经验调幅调频分解及Teager能量算子法在信号解调及瞬时频率计算中的结果，结果表明了递归希尔伯特变换方法的实用性及精确性。

Recursive Hilbert transform for vibration signal demodulation and instantaneous frequency estimation

Accurately extracting instantaneous amplitude and estimating frequency are important problems in structure parameter identification and health monitoring. Hilbert transform is one of the most commonly used methods for signal demodulation and instantaneous frequency computation. However, it causes significant error when the establishment condition of Bedrosian identity is invalid. As such, a recursive Hilbert transform method is proposed, which regards the pure frequency modulation signal derived in the previous step as a new signal and demodulates the signal recursively. The convergence of the recursive procedures is proved by theoretical analysis. The proposed method is compared to Hilbert transform, empirical AM-FM decomposition, and Teager energy method in simulated signal demodulation or instantaneous frequency computation. The results show a good practicality and accuracy of the recursive Hilbert transform.