The Cramer-Rao bound for pole and amplitude coefficient estimates of damped exponential signals in noise

Abstract

A complete Cramer-Rao bound (CRB) derivation is provided for the case in which signals consist of arbitrary exponential terms in noise. Expressions for the CRBs of the parameters of a damped exponential model with one set of poles and multiple sets of amplitude coefficients are derived. CRBs for the poles and amplitude coefficients are derived in terms of rectangular and polar coordinate parameters. For rectangular parameters it is shown that CRBs for the real and imaginary parts of poles and amplitude coefficients are equal and uncorrelated. In polar coordinates, the angle and magnitude CRBs are also uncorrelated. Furthermore, the CRBs of the pole angles and relative magnitudes are equal and are logarithmically symmetric about the unit circle. >