Effect of windowing and noise on the amplitude and phase estimators returned by the Taylor-based Weighted Least Squares

This paper analyzes the effect of windowing and additive wideband noise on the estimates returned by the real-valued Taylor-based Weighted Least Squares (TWLS) algorithm when applied to noisy sine-wave with constant amplitude and phase. The Taylor's series of the signal time-varying phasor are truncated to the second order and the two-term or three-term Minimum Sidelobe Level (MSL) and Maximum Sidelobe Decay (MSD) windows are considered. Expressions for the estimation variances are derived that hold even when the sine-wave amplitude and phase exhibit slow and limited, but significant, time variations. Then they are compared with the unbiased Cramér-Rao Lower Bounds (CRLBs) for constant parameter sine-waves in order to analyze the estimator statistical efficiency. The accuracies of the derived expressions are verified through computer simulations and validated by experimental results.