Frequency estimation based on discrete Fourier transform and least squares

Abstract

A frequency estimation algorithm of sinusoidal signal was presented. It consists of a coarse frequency estimation followed by fine frequency estimation. Discrete Fourier transform (DFT) determines the coarse frequency estimation and least squares estimator (LSE) makes it possible to get the optimal frequency difference estimation. Subsequently, we derive the relationship between the asymptotic error variance (AEV) and the Cramer-Rao bound (CRB). Simulation results show that the performance of the proposed algorithm approaches the CRB of the sinusoid when the signal-to-noise ratio (SNR) is higher than the SNR threshold.