结合信号谐波特性的均值参数测量窗设计  

Designing Mean Parameter Measurement Window Based on Signal Harmonic Characteristics

作　　者：陈砚圃 解云虹 周秦武[3] 丁海洋 CHEN Yanpu;XIE Yunhong;ZHOU Qinwu;DING Haiyang(College of Information Engineering, Xijing University, Xi’an 710123, China;Information and Communications Institute, National University of Defense Technology, Xi’an 710106, China;Key Laboratory of Biomedical Information Engineering of Ministry of Education, Xi’an Jiaotong University, Xi’an 710049, China)

机构地区：[1]西京学院信息工程学院,西安710123 [2]国防科技大学信息通信学院试验训练基地,西安710106 [3]西安交通大学生物医学信息工程教育部重点实验室,西安710049

出　　处：《西安交通大学学报》2022年第5期191-198,共8页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(61871387)。

摘　　要：为了有效抑制准周期信号均值类参数测量时由信号频率的起伏变化和对信号的非同步采样引入的误差,对加窗函数采用组合余弦表示并结合周期信号频谱的谐波特性,提出了一种用于准周期信号均值类参数高精度测量的加窗函数设计方法。首先,基于测量误差在采样同步时为零,并对采样不同步不敏感,分别导出了组合余弦窗的有效条件及其优化设计的平坦性准则;进而以平坦性准则为约束建立了组合余弦窗的系数方程组;最后通过求解方程组确定组合余弦窗的系数,实现了组合余弦窗的优化设计。采用优化组合余弦窗对信号加窗,能够最大限度地抑制各谐波之间的泄漏干扰,显著降低了均值类参数的测量误差。基于组合余弦窗的平坦性准则对广为应用的矩形卷积窗的最优性进行了分析,揭示出在各信号谐波频点处矩形卷积窗的频谱满足相同的平坦性。对典型信号有效值的测量进行数值模拟表明:信号频率在±10%之内起伏变化时,与同宽的矩形卷积窗相比,采用窗宽为2个和3个信号周期的优化组合余弦窗后测量精度分别提高了11倍和27.5倍以上。To control the errors caused by the frequency fluctuation and non-synchronous sampling in measuring mean parameters of the quasi-periodic signal,the window function is represented by combined cosines,and a window function design approach for precisely measuring mean parameters of the quasi-periodic signal is proposed here based on harmonic characteristics of the periodic signal spectrum.Firstly,effective conditions for a combined cosine window and flatness criteria for its optimization design are derived respectively on the basis that the measurement error is zero in the case of synchronous sampling and is insensitive to non-synchronous sampling.And then,the equations for the coefficient of the combined cosine window are created with the constraint of flatness criteria.Finally,these equations are solved to determine the coefficient,thus optimizing the design of the combined cosine window.By windowing the signal with the optimized combined cosine window,it can minimize the leakage interference between harmonics and significantly reduce the measurement error of mean parameters.Widely used rectangular convolution windows are analyzed for optimality based on the flatness criteria,and the analysis results show that the spectra of all these windows are equally flat at each signal harmonic frequency.The numerical simulation of typical signal RMS measurement shows that when the signal frequency fluctuates within±10%,compared with the rectangular convolution window of the same width,the measurement accuracy is improved by more than 11 times and 27.5 times respectively after using the optimized combined cosine windows with the widths of 2 and 3 signal periods.

关 键 词：参数测量 非同步采样 频谱泄漏 矩形卷积窗 组合余弦窗 

分 类 号：TN911.6[电子电信—通信与信息系统]