High-precision Frequency Estimation Based on Iterative DTFT Interpolation

Abstract

To achieve a high-precision frequency estimation of the noisy real sinusoidal signals with any cycles in record, this paper proposes a novel frequency estimation algorithm based on the iterative discrete-time Fourier transform (DTFT) interpolation, breaking the limitation that the existing interpolation algorithm only considers the fixed and equal interval discrete Fourier transform (DFT) spectrum. First, the spectrum transformation is extended to any generalized DTFT spectrum, and a 3-spectral line equation suitable for any spectral interval is obtained by calculation. Then, a multi-spectral line equation set is constructed according to the intervals of the auxiliary spectral lines, and the analytical solution of the unbiased frequency estimation based on different interpolation methods can be obtained. Finally, considering the influence of the additive noise, a simple and effective iterative execution method is used to further optimize the performance of the algorithm to ensure that the mean square error (MSE) of the frequency estimation can be uniformly approximated to the optimum in the entire domain. Simulation analysis and experimental results verify the effectiveness and accuracy of the algorithm.