High resolution spectral analysis of mixtures of complex exponentials modulated by polynomials

Abstract : 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. In this paper, we introduce a more general class of signals, involving both amplitude and frequency modulations. We show that this Polynomial Amplitude Complex Exponentials (PACE) model is the most general model tractable by high resolution methods. We develop a generalized ESPRIT algorithm for estimating the signal parameters, and we show that this model can be characterized by means of a geometrical criterion.
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Roland Badeau, Bertrand David, Gaël Richard. High resolution spectral analysis of mixtures of complex exponentials modulated by polynomials. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2006, 54 (4), pp.1341-1350. ⟨10.1109/TSP.2006.870556⟩. ⟨hal-00479781⟩

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