An algebraic frequency estimator for a biased and noisy sinusoidal signal

An algebraic approach is proposed for the fast and reliable, on line, identification of the amplitude, frequency and phase parameters in unknown noisy sinusoidal signals. The proposed method uses the algebraic derivative method in the frequency domain yielding exact formulae, when placed in the time domain, for the unknown parameters. These formulae are synthesized in terms of time-varying linear unstable filters in combination with classical low-pass filters of the Butterworth type. The computations are performed in a quite small time interval which is only a small fraction of the first full cycle of the measured sinusoid signal. The method is also verified to be robust with respect to signal measurement noises and structured perturbations via digital computer simulations and, also, via actual laboratory experiments.