Three-point Frequency Tracking Method

Abstract

This paper presents and evaluates in detail a harmonics tracking method (HTM) for tracking the instantaneous frequency and amplitude of a vibration signal by processing only three most recent data points. Teager—Kaiser algorithm (TKA) is a popular four-point method for online frequency tracking, but its accuracy is easily destroyed by measurement noise due to the use of finite difference. Moreover, because a signal is assumed to be a pure harmonic in TKA, any moving average in the signal can destroy the accuracy of TKA. On the other hand, HTM uses a constant and a pair of harmonics to fit three recent data points and estimate the instantaneous frequency and amplitude, and it dramatically reduces the influence of any moving average. Moreover, noise filtering is an implicit capability of HTM even if only three points are processed, and this capability increases with the number of processed points. However, HTM depends on TKA to provide the first frequency estimation in order to start online tracking. To compare HTM and TKA and evaluate the accuracy of HTM, Hilbert— Huang transform (HHT) is used to extract accurate time-varying frequency and amplitude by processing the whole data set without assuming the signal to be harmonic. Frequency and amplitude tracking of different amplitude- and/or frequency-modulated signals and nonlinear nonstationary dynamic signals is studied. Results show that HTM is more accurate, robust, and versatile than TKA for online frequency tracking. Moreover, the frequencies and amplitudes tracked by HTM have about the same accuracy as those extracted by HHT, but without the edge effect that HHT suffers from.