A Frequency-Locked-Loop Filter for Biased Multi-Sinusoidal Estimation

In this paper, an adaptive filter, based on a third-order generalized integrator, is proposed to estimate all the parameters of a biased sinusoid. The averaging theory is used to prove that the filter identifies the unknown frequency of the signal, in the case of a pure biased sinusoid in input. Moreover, in the case of a generic periodic signal, the method provides an estimate of the fundamental frequency by converging to a limit cycle in its vicinity. The robustness of the proposed approach with respect to noise in the input signal is analyzed. A filter bank is also presented to deal with the reconstruction problem of a generic multi-sinusoidal signal. Simulation results are also provided to compare the performances of the method with existing ones.