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A common problem, arising in many different applied contexts, consists inestimating the number of exponentially damped sinusoids whose weighted sum bestfits a finite set of noisy data and in estimating their parameters. Manydifferent methods exist to this purpose. The best of them are based onapproximate Maximum Likelihood estimators, assuming to know the number ofdamped sinusoids, which can then be estimated by an order selection procedure.As the problem can be severely ill posed, a stochastic perturbation method isproposed which provides better results than Maximum Likelihood based methodswhen the signal-to-noise ratio is low. The method depends on somehyperparameters which turn out to be essentially independent of theapplication. Therefore they can be fixed once and for all, giving rise to ablack box method.

A black box method for solving the complex exponentials approximation problem