Parameter estimation of a decaying exponential in noise

The estimation of the parameters of a decaying complex exponential in noise was examined by Bertocco et al. who developed a frequency domain interpolator using two DFT coefficients around the maximum bin. Quinn, on the other hand, and more recently Aboutanios and Mulgrew (A&M), proposed similar frequency estimators for the undamped case. In this paper, we adapt the Quinn and A&M algorithms to the decaying case and show that Quinn´s estimator is a linearised version of Bertocco´s. We analyse the theoretical performance of the algorithms and derive approximate expressions for their estimation variances at the bin centre. It is found that, as in the undamped case and unlike the other estimators, the Asimilar frequency estimators for the undamped case. In this paper, we adapt the Quinn and A&M algorithms to the decaying case and show that Quinn´s estimator is a linearised version of Bertocco´s. We analyse the theoretical performance of the algorithms and derive approximate expressions for their estimation variances at the bin centre. It is found that, as in the undamped case and unlike the other estimators, the A&M algorithm exhibits its lowest variance at this point. Thus, implementing it iteratively leads to an improvement in its estimation variance. The theoretical results are verified by simulations and compared to the Cramer-Rao bound.