Frequency estimation of a sinusoidal signal via a three-point interpolated DFT method with high image component interference rejection capability

Abstract

This paper proposes a three-point Interpolated Discrete Fourier Transform (IpDFT) method for frequency estimation of a discrete-time sinusoidal signal. It is based on the maximum sidelobe decay (MSD) windows and is highly effective in rejecting the detrimental effect on the estimation accuracy due to the image component of the signal spectrum. This remarkable feature is achieved by using an analytical expression based on a suitable weighting of the three largest DFT spectrum samples. The proposed method provides good results when the effect of the spectral interference due to the image component dominates other estimation error sources. The accuracy of the proposed method and of other state-of-the-art methods such as the multi-point IpDFT methods and the four-parameter sine-fitting (4PSF) algorithm are compared through both computer simulations and experimental results in the case of ideal, noisy, and harmonically distorted sinusoids. A small number of acquired cycles is assumed in order to analyze situations in which the contribution from the image component interference is significant. The performed comparison shows that the proposed method outperforms the considered multi-point IpDFT methods when the Signal-to-Noise Ratio (SNR) is higher than 30 dB and the number of acquired cycles is enough small. The proposed method outperforms also the 4PSF algorithm when the frequency estimation error is dominated by harmonics rather than wideband noise.