Analytical solutions for frequency estimators by interpolation of DFT coefficients

•Introduce a new set of unbiased analytical estimators for the frequency of cisoid.•Experiments show that the new estimators are more accurate than the previous estimators.•With noise, some estimators work better at low frequency offset and vice versa.

For the estimation of the frequency of a complex sinusoid, previous methods interpolate DFT coefficients to obtain the frequency offset. Most of these interpolation methods can be considered as linear approximation of a nonlinear function. Up to date, only a few previously proposed estimators have been shown to have analytical expressions. In this paper, we show that almost all the interpolated estimators proposed to date, both direct and iterative, have simple analytical solutions for the frequency offset. Thus, the estimation bias of these estimators can be better understood and a whole new set of unbiased estimators using the analytical solutions is also introduced.