Impact of harmonics on the interpolated DFT frequency estimator

• The expression for the frequency estimation error is derived.
• The expression for the combined variance of the frequency estimator is derived.
• A procedure for frequency estimation is proposed.
• The performance of the proposed procedure is compared with those of other methods.
• Theoretical results are confirmed through both simulation and experimental results.

The paper investigates the effect of the interference due to spectral leakage on the frequency estimates returned by the Interpolated Discrete Fourier Transform (IpDFT) method based on the Maximum Sidelobe Decay (MSD) windows when harmonically distorted sine-waves are analyzed. The expressions for the frequency estimation error due to both the image of the fundamental tone and harmonics, and the frequency estimator variance due to the combined effect of both the above disturbances and wideband noise are derived. The achieved expressions allow us to identify which harmonics significantly contribute to frequency estimation uncertainty. A new IpDFT-based procedure capable to compensate all the significant effects of harmonics on the frequency estimation accuracy is then proposed. The derived theoretical results are verified through computer simulations. Moreover, the accuracy of the proposed procedure is compared with those of other state-of-the-art frequency estimation methods by means of both computer simulations and experimental results.