Frequency Estimation by Interpolation of Two Fourier Coefficients: Cramér-Rao Bound and Maximum Likelihood Solution

Sinusoidal frequency estimation in the presence of white Gaussian noise plays a major role many engineering fields. Significant research this area has been devoted to fine tuning stage, where discrete Fourier transform (DFT) coefficients observation data are interpolated acquire residual error $\varepsilon $ . Iterative interpolation schemes have recently designed by employing two notation="LaTeX">$q$ -shifted spectral lines symmetrically placed around DFT peak, and impact on accuracy theoretically assessed. Such analysis, however, is available only for some specific algorithms mostly conducted under assumption vanishingly small error, which makes it inappropriate first stage any iterative process. In work, further investigation carried out examine issues that still open. We start evaluating Cramér-Rao bound (CRB) recovery assess its dependence primary importance check whether existing can provide efficient estimates at iteration or not. After determining optimum value given , we eventually derive maximum likelihood (ML) interpolator. Since latter exhibits best performance step process, might attain desired just end iteration, especially advantageous terms computational load processing time.