Cramér-Rao bound for estimates of frequencies and damping factors of real superimposed signals with multiple poles in noise

Slivinskas, Vytautas; Šimonytė, Virginija

doi:10.1007/bf00992614

Cited by 2 publications

(1 citation statement)

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“…An analysis of the Cramér-Rao bounds for the frequencies and damping factors of complex quasipolynomials with multiple poles in white noise was first proposed in [21] (real quasipolynomials were addressed in [31]). Here the investigation is extended to the Cramér-Rao bounds for the amplitudes and phases of complex polynomials, and to the case of colored noise.…”

Section: Introductionmentioning

confidence: 99%

CramÉr–Rao Bounds for Multiple Poles and Coefficients of Quasi-Polynomials in Colored Noise

Badeau¹,

David²,

Richard³

2008

IEEE Trans. Signal Process.

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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.

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Section: Introductionmentioning

confidence: 99%