A simple estimator for frequency and decay rate

A simple, computationally inexpensive algorithm is developed for estimating the frequency and decay rate of a complex exponential. Two iterations of the algorithm attains the Cramer-Rao bound on the variance of the frequency and decay rate estimate for a complex exponential in white Gaussian noise. The algorithm uses an adaptive window that changes its shape with the estimate of the decay rate. Formulas are derived for the bias and variance of the estimator, and its performance is demonstrated in simulations