Explicit Frequency Estimation and Tracking Using Modulated Lagrange Delay filter

In this paper, we present a new computationally efficient and accurate so-called explicit modulated Lagrange adaptive frequency estimation (EMLAFE) algorithm that is based on a variable delay element of Etter and Hush and the modulated Lagrange adaptive frequency estimator (MLAFE) of Dooley and Nandi. Adopting a similar idea as in So et. al., on explicit time delay estimation, we introduce explicit frequency estimation in our EMLAFE algorithm in order to speed up the frequency estimation. Our development of the EMLAFE algorithm is based on the fact that the cost function of the modulated Lagrange interpolation delay filter (MLIDF), which is used as a FIR delay system in the frequency estimator, is sinusoidal in form with respect to the product of signal frequency and time delay under a high signal to noise ratio (SNR) condition. This leads to a simple formula relating the estimated delay to the unknown frequency, and thus to an efficient frequency estimator. The superior performance of the new algorithm is demonstrated in the context of tracking and estimating a chirp or constant frequency signal in noise. We also derive the Cramer-Rao bound and the steady state variance, for the frequency estimate