Frequency estimation of multi-sinusoidal signal by multiple integrals

In this paper, a simple and robust method for frequency estimation of multi-sinusoidal signal from a given discrete sequence of noisy data is proposed. The approach used herein is based on the algebraic derivative method in the frequency domain and it does not make any assumption on the way to collect the samples of the considered signal. The frequencies are estimated without iterations, and explicit relationship between the elementary symmetric functions on the frequencies of the signal and its multiple integrals is given. Due to the use of the process output integrals, the resulting parameters estimation is very robust in the face of large measurement noise in the output. Moreover, for an easy time realization of the estimation, a time-varying linear (unstable) filter is proposed. Finally, the effectiveness of the proposed method is demonstrated through practical and simulated experiments.