A closed form frequency estimator for a noisy sinusoid

Based on the linear prediction property of sinusoidal signals, a closed form unbiased frequency estimator for a real sinusoid in white noise is proposed. The frequency estimate derives from minimizing a constrained least squares cost function and it is simple to implement either in batch or recursive mode. The relationship of the proposed method with the well-known Pisarenko harmonic decomposer (PHD) is also examined. Computer simulations are included to contrast the estimator performance with the PHD as well as the Cramer-Rao lower bound.