Frequency estimation algorithm for multi-frequency real signals based on spectrum leakage correction

PDF(1369 KB)

Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (15) : 107-113.

CHEN Peng1,2, ZHAO Shaomei2, CHEN Qin1,2, XIE Zhijun2, CHEN Xiaohui2, TU Yaqing3

Author information +

History +

Abstract

Here, in order to suppress effects of negative frequency spectrum leakage and mutual leakage among positive frequency spectra in multi-frequency real signals on frequency estimation, a frequency estimation algorithm based on spectrum leakage correction was proposed. Firstly, FFT method was used to preprocess a sampled signal, and obtain the spectrum index of various components, and then the signal spectrum was interpolated and analyzed to construct spectrum interpolations of all negative frequencies and positive frequencies not to be estimated. Secondly, constructed spectrum interpolations were subtracted from signal spectrum interpolations using the subtraction strategy to obtain spectrum interpolations without spectrum leakage for positive frequencies to be estimated, and then the spectrum offset estimation value of each component was obtained by analyzing generated spectrum interpolations. Finally, accurate estimated values of frequency, amplitude and initial phase of each component were obtained with iterative calculation. The simulation results under different frequency intervals and different SNRs showed that the proposed algorithm has good frequency estimation performance, it can effectively suppress effects of spectrum leakage, improve frequency estimation accuracy of multi-frequency real signals, and make the mean square error of frequency estimation value closer to Cramer-Rao low Bound; ranging tests are conducted on LFMCW radar test platform to verify the practical application effect of the proposed algorithm.

Key words

frequency estimation / spectrum leakage correction / multi-frequency real signal / LFMCW radar

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

CHEN Peng, ZHAO Shaomei CHEN Qin, XIE Zhijun, CHEN Xiaohui, TU Yaqing. Frequency estimation algorithm for multi-frequency real signals based on spectrum leakage correction[J]. Journal of Vibration and Shock, 2021, 40(15): 107-113

References

［1］杜亚震，王文华，黄一. 基于增量谐波平衡方法的Spar平台垂荡纵摇耦合内共振响应研究［J］.振动与冲击，2020，39(1)：85-90.
DU Yazhen, WANG Wenhua, HUANG Yi. Swing-pitch coupled internal resonance responses of spar platform based on IHBM［J］. Journal of Vibration and Shock, 2020, 39(1): 85-90.
［2］陈鹏, 涂亚庆, 李明, 等. 基于迭代插值的实复转换频率估计算法［J］. 振动与冲击, 2019, 38(18): 35-39.
CHEN Peng, TU Yaqing, LI Ming, et al. Real-to-complex-transformation frequency estimation algorithm based on iterative interpolation ［J］. Journal of Vibration and Shock, 2019, 38(18): 35-39.
［3］HAMSAPRIYE C K, LAKSHMEESHA V K. Analysis of pisarenko harmonic decomposition-based subNyquist rate spectrum sensing for broadband cognitive radio［J］．Defence Science Journal, 2017, 67(1):80-87.
［4］SO H C, CHAN K W, CHAN Y T, et al. Linear prediction approach for efficient frequency estimation of multiple real sinusoids: algorithms and analyses［J］. IEEE Transactions on Signal Processing, 2005, 53(7):2290-2305.
［5］LI J, LI D, JIANG D, et al. Extended-aperture unitary root MUSIC-based DOA estimation for coprime array［J］. IEEE Communications Letters, 2018:752-755.
［6］HUANG S, ZHANG H J, SUN H, et al. Frequency estimation of multiple sinusoids with three sub-nyquist channels ［J］. Signal Processing, 2017, 139: 96-101.
［7］陈鹏, 涂亚庆, 刘言, 等. 相减策略的实复转换式参数估计算法［J］. 振动与冲击, 2020, 39(21): 211-216.
CHEN Peng, TU Yaqing, LIU Yan, et al. Real-complex conversion parametric estimation algorithm based on subtraction strategy ［J］. Journal of Vibration and Shock, 2020, 39(21): 211-216.
［8］陈鹏, 涂亚庆, 沈艳林, 等. 实复转换式衰减信号参数估计算法［J］. 振动与冲击, 2020, 38(14):53-58.
CHEN Peng, TU Yaqing, SHEN Yanlin, et al. Real-to-complex-transformation parameter estimation algorithm for damped real-value sinusoidal signal ［J］. Journal of Vibration and Shock, 2020, 38(14):53-58.
［9］WEN H , ZHANG J, MENG Z, et al. Harmonic estimation using symmetrical interpolation FFT based on triangular self-convolution window［J］. IEEE Transactions on Industrial Informatics, 2017, 11(1):16-26.
［10］张鸿博，蔡晓峰，鲁改凤.基于双窗全相位FFT双谱线校正的电力谐波分析［J］.仪器仪表学报，2015，36(12)：2835-2841.
ZHANG Hongbo, CAI Xiaofeng, LU Gaifeng. Double-spectrum-line correction method based on double-window all-phase FFT for power harmonic analysis ［J］. Chinese Journal of Scientific Instrument, 2015, 36(12): 2835-2841.
［11］DJUKANOVIC S, POPOVIC V. Efficient and accurate detection and frequency estimation of multiple sinusoids［J］. IEEE Access, 2019, 7:1118-1125.
［12］YE S L, ABOUTANIOS E. Rapid accurate frequency estimation of multiple resolved exponentials in noise［J］. Signal Processing, 2017, 132:29-39.
［13］YE S L, ABOUTANIOS E. An algorithm for the parameter estimation of multiple superimposed exponentials in noise［C］. IEEE International Conference on Acoustics. IEEE, 2015:3457-3461.
［14］AHMET S, KHALID Q. A fast method for estimating frequencies of multiple sinusoidals［J］. IEEE Signal Processing Letters, 2020, 27:386-390.
［15］ABOUTANIOS E, MULGREW B. Iterative frequency estimation by interpolation on fourier coefficients ［J］. IEEE Transactions on Signal Processing, 2005, 53(4): 1237-1242.
［16］KAY S M. Fundamentals of statistical signal processing, volume III (paperback) ［J］. Detection Theory, 1993, 37(4):465-466.


(上接第97页)

［17］VAN HOUT R, RINSKY V, GROBMAN Y G. Experimental study of a round jet impinging on a flat surface: flow field and vortex characteristics in the wall jet［J］. International Journal of Heat and Fluid Flow, 2018, 70: 41-58.
［18］张星星, 陈明, 许光祥, 等. 有限空间中三维壁面紊动射流流动特性试验研究［J］. 水科学进展, 2019, 30(1): 95-103.
ZHANG Xingxing, CHEN Ming, XU Guangxiang, et al. An experimental study on the flow characteristics of a three-dimensional turbulent wall jet in a limited space［J］. Advances in Water Science, 2019, 30(1): 95-103.
［19］ASHFORTH-FROST S, JAMBUNATHAN K, WHITNEY C F. Velocity and turbulence characteristics of a semiconfined orthogonally impinging slot jet［J］. Experimental Thermal and Fluid Science, 1997, 14(1): 60-67.
［20］ASHFORTHFROST S, JAMBUNATHAN K. Effect of nozzle geometry and semi-confinement on the potential core of a turbulent axisymmetric free jet［J］. International Communications in Heat and Mass Transfer, 1996, 23(2):155-162.
［21］ZHANG J P, XU M Y, MI J C. Large eddy simulations of a circular orifice jet with and without a cross-sectional exit plate［J］. Chinese Physics B, 2014, 23(4): 44704.
［22］COOPER D, JACKSON D C, LAUNDER B E, et al. Impinging jet studies for turbulence model assessment—I. Flow-field experiments［J］. International Journal of Heat and Mass Transfer, 1993, 36(10): 2675-2684.
［23］KNOWLES K, MYSZKO M. Turbulence measurements in radial wall-jets［J］. Experimental Thermal and Fluid Science, 1998, 17(1/2): 71-78.
［24］XU Z, HANGAN H. Scale, boundary and inlet condition effects on impinging jets［J］. Journal of Wind Engineering and Industrial Aerodynamics, 2008, 96(12): 2383-2402.
［25］SODJAVI K, MONTAGN B, BRAGANA P, et al. PIV and electrodiffusion diagnostics of flow field, wall shear stress and mass transfer beneath three round submerged impinging jets［J］. Experimental Thermal and Fluid Science, 2016, 70: 417-436.
［26］SENGUPTA A, SARKAR P P. Experimental measurement and numerical simulation of an impinging jet with application to thunderstorm microburst winds［J］. Journal of Wind Engineering and Industrial Aerodynamics, 2008, 96(3): 345-365.
［27］YADAV H, AGRAWAL A. Effect of vortical structures on velocity and turbulent fields in the near region of an impinging turbulent jet［J］. Physics of Fluids, 2018, 30(3): 035107.