Precise sinusoid frequency estimation based on parabolic interpolation

Fine frequency estimation of a single complex sinusoid is considered. We propose to refine the frequency estimation provided by the state-of-the-art methods based on three discrete Fourier transform (DFT) samples around the DFT maximum. To that end, parabolic interpolation of the periodogram peak is used. With the calculation of only three additional periodogram samples, the Cramér-Rao lower bound is met. Moreover, the proposed method's performance does not depend on the frequency displacement. Due to its simplicity, efficiency and low computational burden, the proposed method is suitable for real-time applications.