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

Abstract

The dependence of the Cramer-Rao (C-R) parameter bounds on the signal phases for complex and real valued time-series data models, consisting of damped sinusoids buried in noise, was studied. The C-R bounds on the variance of unbiased estimators of the signal parameters were found to be independent of the phases of all the sinusoids for the complex case. For the real case, the bounds for the parameters of a particular sinusoid were found to depend on the phase of that particular sinusoid and independent of all the other sinusoids.