Online tracking of instantaneous frequency and amplitude of dynamical system response

This paper presents a sliding-window tracking (SWT) method for accurate tracking of the instantaneous frequency and amplitude of arbitrary dynamic response by processing only three (or more) most recent data points. Teager–Kaiser algorithm (TKA) is a well-known four-point method for online tracking of frequency and amplitude. Because finite difference is used in TKA, its accuracy is easily destroyed by measurement and/or signal-processing noise. Moreover, because TKA assumes the processed signal to be a pure harmonic, any moving average in the signal can destroy the accuracy of TKA. On the other hand, because SWT uses a constant and a pair of windowed regular harmonics to fit the data and estimate the instantaneous frequency and amplitude, the influence of any moving average is eliminated. Moreover, noise filtering is an implicit capability of SWT when more than three data points are used, and this capability increases with the number of processed data points. To compare the accuracy of SWT and TKA, Hilbert–Huang transform is used to extract accurate time-varying frequencies and amplitudes by processing the whole data set without assuming the signal to be harmonic. Frequency and amplitude trackings of different amplitude- and frequency-modulated signals, vibrato in music, and nonlinear stationary and non-stationary dynamic signals are studied. Results show that SWT is more accurate, robust, and versatile than TKA for online tracking of frequency and amplitude.