Accurate Frequency Estimation with Fewer DFT Interpolations based on Pad\'e Approximation

TL;DR

This paper introduces a novel frequency estimation method using Padé approximation within the A&M iterative framework, reducing the number of DFT interpolations needed and improving accuracy especially for small sample sizes.

Contribution

It pioneers the application of Padé approximation to frequency estimation, providing a closed-form residual error solution and enhancing estimation performance over existing methods.

Findings

Outperforms state-of-the-art estimators in simulations

Requires fewer DFT interpolations per iteration

Effective for small sample sizes

Abstract

Frequency estimation is a fundamental problem in many areas. The well-known A&M and its variant estimators have established an estimation framework by iteratively interpolating the discrete Fourier transform (DFT) coefficients. In general, those estimators require two DFT interpolations per iteration, have uneven initial estimation performance against frequencies, and are incompetent for small sample numbers due to low-order approximations involved. Exploiting the iterative estimation framework of A&M, we unprecedentedly introduce the Pad\'e approximation to frequency estimation, unveil some features about the updating function used for refining the estimation in each iteration, and develop a simple closed-form solution to solving the residual estimation error. Extensive simulation results are provided, validating the superiority of the new estimator over the state-the-art estimators in wide ranges of key parameters.