Iterative frequency estimation by interpolation on Fourier coefficients

The estimation of the frequency of a complex exponential is a problem that is relevant to a large number of fields. In this paper, we propose and analyze two new frequency estimators that interpolate on the Fourier coefficients of the received signal samples. The estimators are shown to achieve identical asymptotic performances. They are asymptotically unbiased and normally distributed with a variance that is only 1.0147 times the asymptotic Crame´r-Rao bound (ACRB) uniformly over the frequency estimation range.