Comparative study of two digital phase delay estimators with negative frequency contribution

A comparison is drawn between two digital phase delay estimators with negative frequency contribution which are suitable for real signals when the frequency is quite low or close to the Nyquist frequency. The first estimator is based on discrete Fourier transform and the second estimator is based on discrete-time Fourier transform. Using the error theory, the formulas for evaluating the mean square errors of phase delay estimate under noisy conditions by the two estimators are deduced and compared with the Cramer-Rao lower bound. Theoretical analyses and simulation results show that the second estimator is superior to the first one for the case of large spectrum leakage error and can attain optimum performance.