Frequency estimation of combined complex signals with phase difference method

PDF(1513 KB)

Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (19) : 129-135.

LUO Jiufei, ZHENG Mingxuan, LI Jing

Author information +

History +

Abstract

In the traditional time-shifting based phase difference method, the anti-noise performance of the algorithm can be improved by increasing the translation coefficient. However, the estimation accuracy of traditional method is limited due to the phase-wrapping problem probably caused by the random noise, the location of spectral bins and the large translation coefficient. In this paper, the main factors leading to phase wrapping are investigated and their effects on the frequency estimation are analyzed. In order to improve the accuracy of frequency estimation, an estimator based on the phase difference of combined complex signals is proposed. Simulation results show that the proposed algorithm still works and has a better noise immunity than the traditional methods when the translation coefficient exceeds one.
Key words: phase difference method; phase wrapping; frequency estimation; translation coefficient

Key words

phase difference method / phase wrapping / frequency estimation / translation coefficient

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

LUO Jiufei, ZHENG Mingxuan, LI Jing. Frequency estimation of combined complex signals with phase difference method[J]. Journal of Vibration and Shock, 2022, 41(19): 129-135

References

[1] 谢明, 丁康. 离散频谱分析的一种新校正方法[J]. 重庆大学学报, 1995, 18(2): 47-54.
XIE Ming, DING Kang. A new rectifying technique of discrete spectrum analysis[J]. Journal of Chongqing University, 1995, 18(2): 47-54.
[2] Xie M, Ding K. Corrections for frequency, amplitude and phase in a fast fourier transform of a harmonic signal[J]. Mechanical Systems and Signal Processing, 1996, 10(2): 211-221.
[3] 陈奎孚, 王建立, 张森文. 频谱校正的复比值法[J]. 振动工程学报, 2008, 21(3): 314-318.
CHEN Kuifu, WANG Jianli, ZHANG Senwen. Spectrum correction based on the complex ratio of discrete spectrum around the main-lobe[J]. Journal of Vibration Engineering, 2008, 21(3): 314-318.
[4] Offelli C, Petri D. A frequency-domain procedure for accurate real-time signal parameter measurement[J]. IEEE Transactions on Instrumentation and Measurement, 1990, 39(2): 363-368.
[5] Lin H B, Ding K. Energy based signal parameter estimation method and a comparative study of different frequency estimators[J]. Mechanical Systems and Signal Processing, 2011, 25(1): 452-464.
[6] Ding K, Zhu W, Yang Z, Li W. Anti-noise performance and parameter estimation accuracy of FFT and FT discrete spectrum correction[C]. International Congress on Image and Signal Processing, Tianjin, 2009: 1-5.
[7] Lin H B, Ding K. Anti-noise performance of the FT continuous zoom analysis method for discrete spectrum[J]. Chinese Journal of Mechanical Engineering, 2010, 23(6): 774-779.
[8] 谢明, 张晓飞, 丁康. 频谱分析中用于相位和频率校正的相位差校正法[J]. 振动工程学报, 1999, 12(4): 454-459.
XIE Ming, ZHANG Xiaofei, DING Kang. A Phase difference correction method for phase and frequency correction in spectral analysis[J]. Journal of Vibration Engineering, 1999, 12(4): 454-459.
[9] Ding K, Xie M, Zhang X F. Phase difference correction method for phase and frequency in spectral analysis[J]. Mechanical Systems and Signal Processing, 2000, 14(5): 835-843.
[10] 齐国清, 贾欣乐. 基于DFT相位的正弦波频率和初相的高精度估计方法[J]. 电子学报, 2001, 29(9): 1164-1167.
QI Guoqing, JIA Xinle. High-accuracy frequency and phase estimation of single-tone based on phase of DFT[J]. Acta Electronica Sinica, 2001, 29(9): 1164-1167.
[11] 张家军, 张新燕, 陈倩, 等. 基于改进全相位算法的高精度介质损耗角的测量[J]. 电工技术学报, 2020, 35(14): 3097-3104.
ZHANG Jiajun, ZHANG Xinyan, CHEN Qian, et al. High precision dielectric loss angle measurement based on improved all-phase algorithm[J]. Transactions of China Electrotechnical Society, 2020, 35(14): 3097-3104.
[12] Li X, Xie Z, Luo J. Application of the phase difference correct method in rolling bearing fault diagnosis[J]. Journal of Algorithms and Computational Technology, 2017, 11(4): 378-387.
[13] 汤宝平, 陈建波, 章国稳. 基于相位差校正法的全息谱研究[J]. 振动与冲击, 2009, 28(8): 99-102+202.
TANG Baoping, CHEN Jianbo, ZHANG Guowen. Study on holospectrum based on correction of phase difference[J]. Journal of Vibration and Shock, 2009, 28(8): 99-102+202.
[14] 胡文彪, 夏立, 向东阳, 吴正国. 一种改进的基于相位差法的频谱校正方法[J]. 振动与冲击, 2012, 31(1): 162-166.
HU Wenbiao, XIA Li, XIANG Dongyang, WU Zhengguo. An improved frequency spectrum correction method based on phase difference correction method[J]. Journal of Vibration and Shock, 2012, 31(1): 162-166.
[15] 张海涛, 涂亚庆. 计及负频率影响的科里奥利质量流量计信号处理方法[J]. 仪器仪表学报, 2007, 28(3): 539-544.
ZHANG Haitao, TU Yaqing. New signal processing method with negative frequency contribution for Coriolis mass flowmeter[J]. Chinese Journal of Scientific Instrument, 2007, 28(3): 539-544.
[16] 杨辉跃, 涂亚庆, 张海涛, 易鹏. 一种基于SVD和Hilbert变换的科氏流量计相位差测量方法[J]. 仪器仪表学报, 2012, 33(9): 2101-2107.
YANG Huiyue, TU Yaqing, ZHANG Haitao. Phase difference measuring method based on SVD and Hilbert transform for Coriolis mass flowmeter[J]. Chinese Journal of Scientific Instrument, 2012, 33(9): 2101-2107.
[17] Mcmahon DRA, Barrett RF, et al. An efficient method for the estimation of the frequency of a single tone in noise from the phases of discrete Fourier transforms[J]. Signal Process, 1986, 11(2): 169–177.
[18] Zhu L M, Li H X, Ding H, et al. Noise influence on estimation of signal parameter from the phase difference of discrete fourier transforms[J]. Mechanical Systems and Signal Processing, 2002, 16(6): 991-1004.
[19] Harris F J. On the use of windows for harmonic analysis with the discrete Fourier transform[J]. Proceedings of the IEEE, 1978, 66(1): 51-83.
[20] 丁康, 罗江凯, 谢明. 离散频谱时移相位差校正法[J]. 应用数学和力学, 2002, 23(7): 729-735.
DING Kang, LUO Jiangkai, XIE Ming. Time-shifting correcting method of phase difference on discrete spectrum[J]. Applied Mathematics and Mechanics, 2002, 23(7): 729-735.
[21] 黄云志, 徐科军. 基于相位差的频谱校正方法的研究[J].振动与冲击, 2005, 24(2): 77-79+86.
HUANG Yunzhi, XU Kejun. Study on the spectrum correcting method based on phase difference[J]. Journal of Vibration and Shock, 2005, 24(2): 77-79+86.
[22] 丁康, 朱小勇, 谢明, 钟舜聪, 罗江凯. 离散频谱综合相位差校正法[J]. 振动工程学报, 2002, 15(1): 114-118.
DING Kang, ZHU Xiaoyong, XIE Ming, ZHONG Shuncong, LUO Kaijiang. Synthesized correcting method of phase difference on discrete spectrum[J]. Journal of Vibration Engineering, 2002, 15(1): 114-118.
[23] 杨志坚, 丁康. 高斯白噪声背景下时移相位差校正法的频率估计精度分析[J]. 振动工程学报, 2007, 20(3): 274-279.
YANG Zhijian, DING Kang. Accuracy analysis of frequency estimated by applying time-shifting correcting method of phase difference in presence of Gaussian white noise[J]. Journal of Vibration Engineering, 2007, 20(3): 274-279.
[24] Huang X , Xia X G. A fine resolution frequency estimator based on double sub-segment phase difference[J]. IEEE Signal Processing Letters, 2015, 22(8): 1055-1059.
[25] Luo J, Xie Z, Li X. Asymmetric windows and their application in frequency estimation[J]. Journal of Algorithms & Computational Technology, 2015, 9(4): 389-412.
[26] Macleod M D. Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones[J]. IEEE Transactions on Signal Processing, 1998, 46(1): 141-148.
[27] Jain V K, Collins W L, Davis D C. High-accuracy analog measurements via interpolated FFT[J]. IEEE Transactions on Instrumentation and Measurement, 1979, 28(2): 113-122.
[28] Aboutanios E, Mulgrew B. Iterative frequency estimation by interpolation on Fourier coefficients[J]. IEEE Transactions on Signal Processing, 2005, 53(4): 1237-1242.
[29] 高瑞令, 吴晓富, 颜俊, 朱卫平. 改进的DFT正弦信号频率估计[J]. 信号处理, 2014, 30(9): 1071-1077.
GAO Ruiling, WU Xiaofu, YAN Jun, ZHU Weiping. A modified DFT-based frequency estimator for sinusoidal signals[J]. Journal of Signal Processing, 2014, 30(9): 1071-1077.