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

Roland Badeau (1) , Bertrand David (1) , Gael Richard (1)

1 LTCI - Laboratoire Traitement et Communication de l'Information

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.

Keywords: High resolution; Rotational invariance property; ESPRIT; Polynomial modulation; Multiple eigenvalues

Domains: Acoustics [physics.class-ph]; Acoustics [physics.class-ph]

Roland Badeau, Bertrand David, Gael Richard. High resolution spectral analysis of mixtures of complex exponentials modulated by polynomials. IEEE Transactions on Signal Processing, 2006, 54 (4), pp.1341-1350. ⟨10.1109/TSP.2006.870556⟩. ⟨hal-00479781⟩