Accuracy analysis of the normalized frequency estimation of a discrete-time sine-wave by the average-based interpolated DFT method

The normalized frequency of a sine-wave can be estimated by the average of the two estimates achieved using the Interpolated Discrete Fourier Transform (IpDFT) method. This approach is called average-based IpDFT method. The paper investigates the effect of the spectral interference from the image component and additive wideband noise on the accuracy of the normalized frequency estimator provided by the average-based IpDFT method with maximum sidelobe decay windows in the case of a discrete-time sine-wave. The expressions of the maximum of the normalized frequency estimator error due to the spectral interference and variance of the normalized frequency estimator due to the wideband noise are derived. Also, the expression of the combined standard uncertainty of the normalized frequency estimator is derived. The accuracies of all derived expressions are confirmed by means of computer simulations. Moreover, the performance of the average-based IpDFT method is compared with those of a state-of-the-art three-point IpDFT method and IpDFT method through both computer simulations and experimental results.

► We estimate the normalized frequency by average-based interpolated DFT method. ► The effects of spectral interference and wideband noise are evaluated. ► The combined standard uncertainty of the normalized frequency estimator is determined. ► The accuracies of the derived expressions are confirmed through computer simulations. ► Experimental data carried out validate the theoretical results.