The possibility of error reduction in frequency estimations with a multipoint interpolated discrete Fourier transformation (DFT) for the Hanning window is described. An estimation of the periodic parameter by the interpolation of the DFT gives the same effect as the reduction of spectrum tails. Sidelobe suppression is obtained at the cost of widening the main lobe, and this increases noise contributions. In this paper, we try to show a tradeoff between the reduction in systematic error of the frequency estimation and the uncertainty of the estimated results due to the interpolated algorithm. The number of interpolated points depends on the noise level and on the mutual positions of the frequency components of the signal.