Unbiased Sine-wave Frequency Estimation by Parabolic Interpolation of DTFT Samples

In this paper the Parabolic Interpolated Discrete-Time Fourier Transform (PIpDTFT) algorithm proposed for the frequency estimation of a complex-valued sine-wave is extended to signal weighted by a Maximum Sidelobe Decay (MSD) window and its accuracy is analyzed. A criterion is proposed that enables the determination of the maximum distance between the DTFT interpolation points that ensures a negligible estimator bias. Also, the accuracy of the PIpDTFT frequency estimator is analyzed as a function of the accuracy of the used initial frequency estimate. Moreover, the robustness of the PIpDTFT frequency estimator to the spurious tones is investigated and compared with those of different state-of-the-art frequency estimators through computer simulations.