Frequency estimator of sinusoid based on interpolation of three DFT spectral lines

A frequency estimator of sinusoid based on interpolation of three discrete Fourier transform (DFT) spectral lines is proposed. The FFT is performed first on the sampled sinusoid signal and the coarse frequency estimation is made by searching the location of the discrete spectral line with maximum amplitude (the primary spectral line). Fine frequency estimation is made by the interpolation using the primary spectral line and two auxiliary spectral lines located at arbitrary position within the main lobe or the first sidelobe of the frequency spectrum. The formula for calculating the MSE of the proposed estimator in additive white noise is derived. The influence of the interval between the primary spectral line and the auxiliary spectral lines on the MSE is analyzed through theoretical analysis and simulation experiments. To further improve the estimation performance, iterative procedures are used. Simulation results show that the RMSE of the proposed estimator is closer to CRLB than the competing estimators especially at high SNR.