基于基波频率估计的多谐波分析

Multi-harmonics Analysis Based on Fundamental Frequency Estimate

采用自适应陷波滤波器实现基波频率可变的多谐波(包含整数次谐波和非整数次间谐波)分析.算法包括基波频率估计器和多个二维正弦跟踪器,形成缓慢自适应积分流形,用李雅普诺夫定理和平均方法证明积分流形的存在性和稳定性.若滤波器频率系数和信号的谐波结构相同,该自适应陷波滤波器是一致渐近稳定的,可按指数收敛准确跟随基波频率、每个谐波(间谐波)及其幅值.导出了频率特性表达式和频率特性矩阵,分析了滤波器参数对稳态频率特性的影响.通过仿真证实算法的有效性,并说明减小滤波器带宽参数和自适应增益能够获得更好的噪声特性.

An adaptive notch filter is presented to analyze integral and fractional harmonics of variable fundamental frequency. The algorithm is composed of a fundamental frequency estimator and a number of 2-dimensional sinusoid trackers, and forms a slow adaptive integral manifold whose existence and stability are proved by Lyapunov stability theorem and averaging method. If filter＇s frequency parameters are the same as those of the harmonics compositions then it is uniformly asymptotically stable, and the fundamental frequency and harmonics （inter-harmonics） with their amplitudes can be precisely tracked in exponential convergence. The frequency characteristics expression and the characteristic matrix are derived, and the influence of the filter parameters on frequency characteristics is investigated. The validity of the proposed algorithm is verified by simulation and it is pointed out that better noise property can be achieved by decreasing bandwidth and adaptive gain.