On the algebraic identification of the frequencies, amplitudes and phases of two sinusoidal signals from their noisy sum

Abstract

An algebraic identification approach is used for the fast and reliable on-line determination of the defining parameters of two sinusoidal signals of different, unknown, amplitudes, phases and frequencies from their noise-perturbed measured sum. The proposed method is based on the algebraic derivative approach, defined in the frequency domain, yielding exact calculation formulae for the unknown parameters when interpreted in a noise-free time-domain environment. The proposed computation formulae are synthesized in terms of time-varying linear, unstable, filters in combination with classical low-pass filters. The proposed algorithms are insensitive to initial conditions, require no special design parameter tuning and the fast convergence is of non-asymptotic nature. The on-line computations are performed in a time interval which is only a fraction of the first full cycle of one of the integrating components of the measured signal. Several simulations are shown to verify the algorithm proposed. Finally, experimental results dealing with actual laboratory signals are presented.

Acknowledgements

This research was supported by the Spanish Government Research Programme via Project DPI-2003-03326 (MCyT), by the Junta de Comunidades de Castilla-La Mancha and European Social Fund. Dr. Sira-Ramírez’ sabbatical stay in the UCLM was financed by the Spanish Ministry of Education and Science through the Secretaría de Estado de Universidades e Investigación and its Dirección General de Universidades. The authors would like to thank Emiliano Pereira González for helpful comments.