Sensitivity to Frequency Uncertainty of the Estimators Provided by the Two-Parameter Sine-Fit Algorithm

In this article, the contribution of frequency error on the sine-wave amplitude and phase estimators returned by the linear two-parameter sine-fit (2PSF) algorithm is analyzed. Expressions for the mean square errors (MSEs) of both estimators are derived in the case of pure and noisy sine waves assuming that the frequency error is small. From the derived expressions a constraint on frequency uncertainty ensuring that the MSEs of the amplitude and phase estimators reach the corresponding Cramér-Rao Lower Bounds is determined. The derived constraint is applied to two different state-of-the-art Interpolated Discrete Fourier Transform (IpDFT) frequency estimators to determine the number of observed sine-wave cycles above which the linear 2PSF algorithm provides statistical efficient amplitude and phase estimates.