Identification of a sinusoidal signal

This paper discusses the online estimation problem of frequency, amplitude and initial phase of a measured sinusoidal signal by using the adaptive method and filter theory. The proposed method is based on an identity between a sinusoidal signal and its second order derivative. Firstly, the frequency is estimated by using the filters of the measured signal. Secondly, the derivative of the measured signal is estimated. Thirdly, by using the estimates of the frequency and the first order derivative of the signal, the amplitude is estimated. Finally, the initial phase is estimated. The estimation errors converge to zero exponentially. Simulation results show the effectiveness of the proposed new method. The robustness to measurement noises is also demonstrated by computer simulation.