基于通用可调(p,q)阶Rife-Vincent自乘-卷积窗的改进四谱线插值高精度谐波分析算法  

High-precision harmonic analysis algorithm based on improved four-spectral-line interpolation with universal tunable(p,q)order Rife-Vincent self-multiplication-convolution window

作　　者：雷可君[1,2] 李明皓 汪旭明 张银行 胡力[1] 王向明[3] 杨喜 LEI Kejun;LI Minghao;WANG Xuming;ZHANG Yinhang;HU Li;WANG Xiangming;YANG Xi(School of Communication and Electronic Engineering,Jishou University,Jishou 416000,China;College of Information Science and Engineering,Hunan University,Changsha 410082,China;Shanghai Stock Exchange Technology Co.Ltd.,Shanghai 200120,China)

机构地区：[1]吉首大学通信与电子工程学院,湖南吉首416000 [2]湖南大学信息科学与工程学院,湖南长沙410082 [3]上交所技术有限责任公司,上海200120

出　　处：《中南大学学报（自然科学版）》2023年第10期3926-3936,共11页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(61861019,62161012);湖南省教育厅科研项目(21A0335,22C0287)。

摘　　要：加窗快速傅里叶变换(WIFFT)是一类重要的谐波参数估计方法。然而,快速傅里叶变换固有的栅栏效应以及非同步采样产生的频谱泄漏对谐波参数的估计精度有较大影响。为此,利用具有最大旁瓣衰减特性的I类Rife-Vincent窗作为父窗,提出一种新型的通用可调(p,q)阶Rife-Vincent自乘-卷积窗(RVSMC p-q),其特点在于通过改变乘积阶数和卷积阶数可以灵活地改变窗函数的主瓣宽度、旁瓣峰值和衰减速度。在此基础上,提出一种基于RVSMC p-q窗的四谱线插值高精度谐波参数估计方法,利用最小二乘拟合原理给出谐波信号的幅值、频率及相位参数的低复杂度多项式估计公式。在复杂谐波、间谐波及基波频率波动的情况下对基于RVSMC p-q窗的四谱线插值谐波参数估计方法的效果进行仿真。研究结果表明:在较低的乘积和卷积阶数条件下,新算法可以获得比经典的基于自乘积窗或自卷积窗的WIFFT算法更为优越的参数估计精度,且算法复杂度较低。The windowed fast Fourier transform(WIFFT)is one of the most important harmonic parameter estimation methods.However,the inherent fence effect of FFT and the spectrum leakage caused by asynchronous sampling seriously affect the estimation accuracy of harmonic parameters.Therefore,a universal tunable(p,q)order Rife-Vincent self-multiplication-convolution window(RVSMC p-q)was proposed by using class I Rife-Vincent window with maximum decay as the parent window.The mainlobe width,sidelobe peak value and sidelobe attenuation speed of RVSMC p-q window can be flexibly controlled by changing the multiplication order and the convolution order.On this basis,a high-precision harmonic parameter estimation method based on four spectral line interpolation by using RVSMC p-q window was proposed.The low complexity polynomial estimation formulas corresponding to the amplitude,frequency and phase of harmonic signals were given via the least square fitting.Experimental simulations were conducted to evaluate the performance of the proposed harmonic parameter estimation method based on the four spectral line interpolation by using RVSMC p-q window in the case of complex harmonics,interharmonics and fundamental wave frequency fluctuations.The results show that the proposed algorithm can achieve better estimation accuracy than the classical WIFFT algorithms based on self-multiplication or self-convolution window even under the condition of low orders of multiplication and convolution,and the algorithm complexity of the new algorithm is relatively low.

关 键 词：谐波分析 参数估计 (p q)阶Rife-Vincent自乘-卷积窗(RVSMC p-q) 四谱线插值 低复杂度 

分 类 号：TN911.72[电子电信—通信与信息系统] TM935.1[电子电信—信息与通信工程]