Cramer-Rao bounds for deterministic modal analysis

Cramer-Rao bounds are computed for any unbiased estimator of the mode parameters that characterize an autoregressive moving average impulse response. The bound can be computed for any of the standard parametric descriptions, including autoregressive moving average parameters, poles and residues, and poles and zeros. It is demonstrated that the bounds for any characterization can be obtained from any other characterization via simple transformations. Asymptotic, frequency domain versions of the Cramer-Rao bounds are also derived. The bound is computed for a fourth-order system to illustrate the coupling between estimation errors and illuminate the influence of mode locations on the ability to identify mode parameters