  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.
