Asymptotic Cramer-Rao bounds for estimation of the parameters of damped sine waves in noise

摘要

The problem of estimating the parameters of a signal composed of several damped sine waves in noise has applications, for example, in transient signal analysis. Explicit, closed-form expressions are derived for the Cramer-Rao bound of this problem in the case of low damping, low spectral interference between the signal components, and a sufficiently large number of samples. Among several conclusions which are drawn from the expressions, it is found that the estimation problem is much more sensitive to errors in the damping factor and frequency than to errors in amplitude and phase.