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High-resolution methods such as the ESPRIT algorithm are of major interest for estimating discrete spectra, since they overcome the resolution limit of the Fourier transform and provide very accurate estimates of the signal parameters. In signal processing literature, most contributions focus on the estimation of exponentially modulated sinusoids in a noisy signal. This paper introduces a more general class of signals, involving both amplitude and frequency modulations. It shows that this Polynomial Amplitude Complex Exponentials (PACE) model is the most general model tractable by high-resolution methods. A generalized ESPRIT algorithm is developed for estimating the signal parameters, and it is shown that this model can be characterized by means of a geometrical criterion.