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This paper investigates the effect of algorithm error, spectral interference, and additive wideband noise on the accuracy of the normalized frequency estimation provided by the Energy-Based Method (EBM) in the case of a discrete-time sine-wave. The statistical efficiency of the EBM estimator with respect to the unbiased Cramér-Rao Lower Bound (CRLB) is determined. The accuracy of the derived expressions is confirmed by means of computer simulations. Moreover, the expression of the rms error of the normalized frequency estimate is derived. Finally, the performance of the normalized frequency estimators provided by the EBM and other state-of-the-art methods are compared by means of both simulations and experimental results.