Performance of ESPRIT for Estimating Mixtures of Complex Exponentials Modulated by Polynomials

High-resolution (HR) methods are known to provide accurate frequency estimates for discrete spectra. The polynomial amplitude complex exponentials (PACE) model, also called quasi-polynomial model in the literature, was presented as the most general model tractable by HR methods. A subspace-based estimation scheme was recently proposed, derived from the classical ESPRIT algorithm. In this paper, we focus on the performance of this estimator. We first present some asymptotic expansions of the estimated parameters, obtained at the first order under the assumption of a high signal-to-noise ratio (SNR). Then the performance of the generalized ESPRIT algorithm for estimating the parameters of this model is analyzed in terms of bias and variance, and compared to the Cramer-Rao bounds (CRB). This performance is studied in an asymptotic context, and it is proved that the efficiency of undamped single poles estimators is close to the optimality. Moreover, our results show that the best performance is obtained for a proper dimensioning of the data. To illustrate the practical capabilities of the generalized ESPRIT algorithm, we finally propose an application to ARMA filter synthesis, in the context of system conversion from continuous time to discrete time.