On fitting exponentially damped sinusoids

There is an enormous literature associated with the estimation of the parameters of a sinusoid in additive noise. While there has been less work devoted to the estimation of the parameters of noisy sinusoids with exponentially damped amplitudes, the two problems have equally long histories, with a common solution proposed by Prony in 1795 [1]. Most of the modern approaches to the problem involve the use of sample autocovariances. In this paper, we review the nonlinear regression based approaches, and describe and analyse a 'frequency-domain' approach that is inherently much more accurate than the covariance-based approach, but which is also computationally efficient, extending the work of Aboutanios [2].