THE CRAMER-RAO BOUND FOR POLE AND AMPLITUDE COEFFICIENT ESTIMATES OF DAMPED EXPONENTIAL SIGNALS IN NOISE

This paper provides a complete Cramer-Rao bound (CRB) derivation for the case where signals consist of arbitrary exponential terms in noise. Expressions for the CRB's of the parameters of a damped exponential model with one set of poles and multiple sets of amplitude coefficients are derived. CRB's for the poles and amplitude coefficients are derived in terms of both rectangular and polar coordinate parameters. In rectangular parameters it is shown that the real and imaginary part CRB's for both the poles and amplitude coefficients are equal and uncorrelated. In polar coordinates the angle and magnitude CRB's are also uncorrelated; furthermore, the CRB's of the pole angles and relative magnitudes are equal, and are logarithmically symmetric about the unit circle.