Multi-harmonics Analysis Based on Fundamental Frequency Estimate
基于基波频率估计的多谐波分析

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.