Accuracy analysis of the amplitude estimation of a sine-wave by the energy-based method using the direct and indirect procedures

The energy-based method (EBM) can be used to estimate the amplitude of a sine-wave either directly from Discrete Fourier Transform (DFT) samples or indirectly. In this paper the accuracies achieved with both these approaches are compared when some of the most commonly used cosine class windows are adopted. The effect on the estimation accuracy of the algorithm error, the spectral interference from the image component, and wideband noise superimposed to the sine-wave signal are separately evaluated and compared. The statistical efficiencies of both procedures with respect to the unbiased single-tone Cramér-Rao lower bound are determined and compared. Moreover, the overall root mean square of the amplitude estimation error achieved when taking into account all the three contributions above is derived for both direct and indirect estimation procedures. The accuracy of the obtained expressions is verified by means of computer simulations. Besides, experimental data validate the theoretical results.

► We estimate the amplitude by the energy-based method. ► Both the direct and indirect procedures are analyzed. ► The effects of algorithm error, spectral interference, and noise are evaluated. ► The accuracies of the derived expressions are confirmed through computer simulations. ► Experimental data validate the theoretical results.