On the phase dependence of the Cramer-Rao bounds for damped sinusoids

Abstract

The problem of estimating the parameters of superimposed damped sinusoids in noise is considered for both complex and real data cases. It is shown that for the complex case, the Cramer-Rao bounds on the variance of unbiased estimators of the signal parameters are independent of the phases of all the sinusoids, and that for the real case, the bounds for the parameters of a particular sinusoid are dependent on the phase of that sinusoid, but are independent of the phases of all the other sinusoids.