Sinusoid frequency estimator with parabolic interpolation of periodogram peak

Abstract

The paper considers periodogram maximization-based frequency estimation of a single complex sinusoid. We propose to improve the accuracy of recently proposed methods based on three discrete Fourier transform (DFT) samples around the DFT maximum. For that purpose, a three-point parabolic interpolation of the periodogram peak is used. The proposed method requires the calculation of only two additional periodogram samples, yielding the accuracy that meets the Cramer-Rao lower bound. In addition, the performance of the method practically does not depend on the frequency displacement. Due to its straightforward implementation, efficiency and low calculation complexity, the method is well suited for applications that require fast and precise frequency estimation.