In this paper, we provide analytical expressions of the Cramér-Rao bounds for the frequencies, damping factors, amplitudes and phases of complex exponentials in colored noise. These expressions show the explicit dependence of the bounds of each distinct parameter with respect to the amplitudes and phases, leading to readily interpretable formulae, which are then simplified in an asymptotic context. The results are presented in the general framework of the Polynomial Amplitude Complex Exponentials (PACE) model, also referred to as the quasipolynomial model in the literature, which accounts for systems involving multiple poles, and represents a signal as a mixture of complex exponentials modulated by polynomials. This work looks further and generalizes the studies previously undertaken on the exponential and the quasipolynomial models.

Abstract-This paper proposes an extension of the applicability of phase-vocoder-based frequency estimators for generalized sinusoidal models, which include phase and amplitude modulations. A first approach, called phase corrected vocoder (PCV), takes into account the modification of the Fourier phases resulting from these modulations. Another approach is based on an adaptation of the principles of the time-frequency reassignment and is referred to as the reassigned vocoder (RV). The robustness of the estimation against noise is studied, both theoretically and experimentally, and the performance is assessed in comparison with two state-of-the-art algorithms: an unmodified version of the reassignment method and a quadratically interpolated fast Fourier transform method (QIFFT).Index Terms-AM/FM model, frequency estimation, phase vocoder.

In this paper we provide a formal justification of the use of time-frequency reassignment techniques on time-frequency transforms of discrete time signals.State of the art techniques indeed rely on formulae established in the continuous case which are applied, in a somehow inaccurate manner, to discrete time signals.Here, we formally derive a general framework for discrete time reassignment. To illustrate its applicability and generality, this framework is applied to a specific transform: the Constant-Q Transform.