Cramer-Rao bounds for deterministic modal analysis

The accuracy with which deterministic modes can be identified from a finite record of noisy data is determined by computing the Cramer-Rao bound on the error covariance matrix of any unbiased estimator of mode parameters. The bound is computed for many of the standard parametric descriptions of a mode, including autoregressive and moving-average parameters, poles and residues, and poles and zeros. Asymptotic, frequency-domain versions of the Cramer-Rao bound bring insight into the role played by poles and zeros. Application of the bound to second- and fourth-order systems illustrates the influence of mode locations on the ability to identify them. Application of the bound to the estimation of an energy spectrum illuminates the accuracy of estimators that presume to resolve spectral peaks