Estimating the frequency of a noisy sinusoid by linear regression (Corresp.)

The estimation of the parameters of a sinusoid from observations of signal samples corrupted by additive noise is investigated. At high signal-to-noise ratios the additive noise is viewed as an equivalent phase noise, suggesting frequency and phase estimation by linear regression on the signal phase. The variances of the regression estimates are shown to achieve the Cramer-Rao bounds. A formula for the variance of the regression frequency estimator is derived in terms of the noise power spectrum. A simple formula for the variance with
1/f^{2}
phase noise is presented.