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

机译:噪声中阻尼指数信号的极点和振幅系数估计的Cramer-Rao界

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摘要

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.
机译:对于信号包含噪声中任意指数项的情况,提供了完整的Cramer-Rao界(CRB)推导。推导了具有一组极点和多组振幅系数的阻尼指数模型参数的CRB表达式。极点和振幅系数的CRB是根据直角坐标和极坐标参数得出的。对于矩形参数,表明极点的实部和虚部的CRB和振幅系数均相等且不相关。在极坐标中,角度和幅度CRB也不相关。此外,极角和相对大小的CRB相等,并且关于单位圆对数对称。

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