Amplitude and Phase Estimation of Real-Valued Sine Wave via Frequency-Domain Linear Least-Squares Algorithms

This paper investigates the real-valued sine-wave amplitude and phase estimates returned by two frequency-domain linear least-squares (FLLSs) algorithms. Both algorithms are based on discrete-time Fourier transform samples evaluated at the sine-wave frequency in order to maximize the immunity to wideband noise. One of the analyzed procedures, called FLLS algorithm, is affected by the contribution of the spectral image component to the estimated parameters. The other one, called the enhanced-FLLS algorithm, compensates for this detrimental contribution, which is particularly significant when a small number of sine-wave cycles is observed. The image component interference compensation is obtained at the cost of a slightly higher computational effort and noise immunity. Closed-form relationships for both the analyzed estimators and their variances are provided. Analytical expressions for the estimators which avoid matrix operations are also derived under conditions of practical interest. Finally, the accuracies of the analyzed algorithms are compared with that of a state-of-the-art estimator based on the classical three-parameter sine-fit algorithm, through both theoretical and simulation results.