Generalised DFT-based estimators of the frequency of a complex exponential in noise

In this paper we consider the estimation of the frequency of a complex exponential in noise. This problem is of prime significance in many signal processing applications. In particular, we focus on robust low computational complexity estimators that rely on the highly efficient FFT algorithm. We generalise a number of interpolators to the zero-padded case and derive both their interpolation expressions and theoretical performance under any amount of zero padding. We also propose a hybrid algorithm that combines the interpolators with the maximisation of a non-linear function of the residual to implement the fine search. Simulation results confirm the improved performance of the proposed algorithms. The hybrid algorithm is found to have a lower estimation variance that is extremely close to the Cramer-Rao bound, while the zero-padded estimators have a lower SNR threshold.