Algebraic parameter estimation of a multi-sinusoidal waveform signal from noisy data

In this paper, we apply an algebraic method to estimate the amplitudes, phases and frequencies of a biased and noisy sum of complex exponential sinusoidal signals. Let us stress that the obtained estimates are integrals of the noisy measured signal: these integrals act as time varying filters. Compared to usual approaches, our algebraic method provides a more robust estimation of these parameters within a fraction of the signal's period. We provide some computer simulations to demonstrate the efficiency of our method.