Dynamics of the frequency estimation in the frequency domain

The possibilities of error reduction of frequency estimation with multi-point interpolated discrete Fourier transform (DFT) for the Hanning window is described. Estimation of the periodic parameter by the interpolation of the DFT gives the same effect as the reduction of the spectrum tails. The side-lobe suppression is at the cost of widening the main lobe, and with this, increasing the noise contributions. In this paper, we try to show a trade off between the reduction of the systematic error of the frequency estimation and the uncertainty of the estimated results due to the interpolation algorithm. The number of interpolated points depends on the noise level, and on the mutual positions of frequency components of the signal.