Estimation of the frequency of a complex exponential

The estimation of the frequency of a complex exponential is relevant to many fields and has been the subject of a significant amount of research. In this paper, we present a novel complex exponential frequency estimation algorithm that is based on the iterative interpolation strategy of Aboutanios and Mulgrew. The A&M algorithm uses two Fourier coefficients and has been shown to reach, in two iterations, a variance that is 0.063 dB above the Cramer-Rao Bound. It, however, requires the calculation of two additional DFT coefficients at each iteration. The new algorithm is computationally simpler as it exploits the standard DFT coefficients at the first iteration. Theoretical analysis and simulation results are presented that demonstrate that the new algorithm maintains the same performance as the A&M estimator.