Windowed iterative estimation of the parameters of a damped complex exponential in noise

The estimation of the frequency and decay factor of a single decaying exponential in noise is an important problem that has commanded significant attention in the research literature. In this paper, we examine the performance of computationally simple, yet accurate and robust, discrete Fourier transform based estimators. These estimators employ a coarse search followed by an interpolation step to obtain precise estimates of the parameters. Although their performance initially improves as the number of samples is increased, it reaches a minimum before departing significantly from the Cramer Rao Lower Bound (CRLB). We tackle this problem in this paper and propose a windowing strategy that allows the estimation performance to track the CRLB for a large number of samples. Furthermore, a practical implementation of the proposed method is given. Extensive simulations are reported that demonstrate the effectiveness of the proposed strategy.