Identification for a signal composed of multiple sinusoids

A very simple on-line identification method for a measured periodic signal composed of multiple sinusoids is discussed. The bias of the signal and the multiple frequencies of the sinusoids are adaptively estimated based on an identity between a sinusoid and its second-order derivative. The amplitudes and the initial phases of the sinusoids are identified using the estimates of the bias and the multiple frequencies based on the state observer theory and state transformation. Simulation results show that the proposed method is effective.