Effect of noise and harmonics on sine-wave frequency estimation by interpolated DFT algorithms based on few observed cycles

In this paper the performances of two state-of-the-art Interpolated Discrete Fourier Transform (IpDFT) algorithms are analyzed when sine-wave frequency must be estimated over short observation intervals. The first estimator, called enhanced IpDFT (e-IpDFT) algorithm, exploits a two-point interpolation and compensates the detrimental contribution of the fundamental image component on the estimated frequency by using an iterative procedure. The second estimator, called IpDFT-EIF algorithm, eliminates that contribution by using a three-point interpolation. Both algorithms reduce the spectral leakage due to time-domain truncation by weighting the acquired signal by a Maximum Sidelobe Decay (MSD) window. The analysis is performed in the case of ideal, noisy, and noisy and harmonically distorted sine-waves. Theoretical expressions for the estimation Mean Square Errors (MSEs) due to noise and harmonics are derived and verified through simulations and experiments. The performed analysis allows the selection of the best frequency estimator for given signal-to-noise-ratio, harmonic content, and number of acquired cycles.