A frequency-domain linear least-squares approach for complex sine-wave amplitude and phase estimation

In this paper new Frequency-domain Linear Least Squares (FLLS) estimators for the amplitude and the phase of a complex noisy sine-wave are proposed. The related estimation variances coincide with the minimum variances returned by the classical FLLS amplitude and phase estimators which occurs when sine-wave is coherently sampled. Simple analytical expressions for both the classical and proposed FLLS amplitude and phase estimators are derived when three Discrete Time Fourier Transform (DTFT) samples are considered and the Maximum Sidelobe Decay (MSD) windows are adopted. These expressions allow us to avoid the matrix implementation of the least-squares approach, thus improving computational efficiency. The obtained results are verified through computer simulations.