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.
胡志祥,任伟新 . 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[J]. 振动与冲击, 2016, 35(7): 39-43.
HU Zhi-xiang,REN Wei-xin . Recursive Hilbert transform for vibration signal demodulation and instantaneous frequency estimation. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(7): 39-43.
[1] 高维成, 刘伟, 邹经湘. 基于结构振动参数变化的损伤探测方法综述[J]. 振动与冲击, 2004, 23(4):1-7, 17.
GAO Wei-cheng, LIU Wei, ZOU Jing-xiang. Damage detection methods based on changes of vibration parameters: A summary review. Journal of vibration and shock, 2004, 23(4): 1-7, 17.
[2] Qian S, Chen D. Joint time-frequency analysis [J]. IEEE Journals and Magazings, 1999, 16(2):52-67.
[3] Ruzzene M, Fasana A, Garibaldi L, Piombo B. Natural frequencies and dampings identification using wavelet transform: Application to real data [J]. Mechanical Systems and Signal Processing, 1997, 11(2):207-218.
[4] Wang C, Ren W, Wang Z, Zhu H. Instantaneous frequency identification of time-varying structures by continuous wavelet transform [J]. Engineering Structures, 2013, 52:17-25.
[5] Ditommaso R, Mucciarelli M, Ponzo F C. Analysis of non-stationary structural systems by using a band-variable filter [J]. Bulletin of Earthquake Engineering, 2012, 10(3):895-911.
[6] Daubechies I, Lu J, Wu H. Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool [J]. Applied and Computational Harmonic Analysis, 2011, 30(2):243:361.
[7] 朱可恒, 希庚, 薛冬新. 希尔伯特振动分解在滚动轴承故障诊断中应用 [J]. 振动与冲击, 2014, 33(14): 160-164.
ZHU Ke-heng, SONG Xi-geng, XUE Dong-xin. Roller bearing fault diagnosis using Hilbert vibration decomposition. Journal of Vibration and Shock, 2014, 33(14): 160-164.
[8] 程军圣, 杨宇, 于德介. 基于广义解调时频分析的多分量信号分解方法 [J]. 振动工程学报, 2007, 20(6): 563-569.
CHENG Jun -sheng, YANG Yu, YU De-jie. A multi-component signal decomposition method based on the general ized demodulation time-frequency analysis. Journal of Vibration Engineering, 2007, 20(6): 563-569.
[9] Qin Y, Qin S, Mao Y. Research on iterated Hilbert transform and its application in mechanical fault diagnosis [J]. Mechanical Systems and Signal Processing, 2008, 22(8):1967-1980.
[10] Huang N E, Shen Z, Long S R and et al. The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis [J]. Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences, 1998, 454(1971):903-995.
[11] Bedrosian E. A product theorem for Hilbert transforms [J]. Proceedings of IEEE, 1963, 51(5): 868–869.
[12] Picinbono B. On instantaneous amplitude and phase of signals [J]. IEEE Transactions on signal processing, 1997, 45(3): 552-560.
[13] Huang N E, Wu Z. A review on Hilbert-Huang transform: method and its applications to geophysical studies [J]. Reviews of Geophysics. 2008, 46(2): RG2006: 1-23.
[14] 张亢, 程军圣, 杨宇, 邹宪军. 基于分段波形的信号瞬时频率计算方法 [J]. 湖南大学学报（自然科学版）, 2011, 38(11): 54-59.
ZHANG Kang, CHENG Jun-sheng, YANG Yu, ZOU Xian-jun. A piece-wise based signal instantaneous frequency computing method. Journal of Hunan University(Natural Sciences), 2011, 38(11): 54-59.
[15] 戴豪民, 许爱强. 瞬时频率计算方法的比较研究和改进 [J]. 四川大学学报（自然科学版）, 2014, 51(6): 1197-1204.
DAI Hao-min, XU Ai-qiang. Comparative research and improvement on the calculation method of instantaneous frequency. Journal of Sichuan University (Natural Sciency Edition), 2014, 51(6):1197-1204.
[16] Alexandros P, Petros M. A comparison of the energy operator and the Hilbert transform approach to signal and speech demodulation [J]. Signal Processing, 1994, 37(1): 95-120.
