On the Phase Dependence of the Cramér-Rao Bounds for Damped Sinusoids

Erdoğan Dilaveroğlu

doi:10.3390/mca7020093

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Article

1 August 2002

On the Phase Dependence of the Cramér-Rao Bounds for Damped Sinusoids

Uludağ University, Department of Electronic Engineering, 16059 Bursa, Turkey

Math. Comput. Appl.2002, 7(2), 93-102;https://doi.org/10.3390/mca7020093

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Abstract

The problem of estimating the parameters of superimposed damped sinusoids in noise is considered for both complex and real data cases. It is shown that for the complex case, the Cramér-Rao bounds on the variance of unbiased estimators of the signal parameters are independent of the phases of all the sinusoids, and that for the real case, the bounds for the parameters of a particular sinusoid are dependent on the phase of that sinusoid, but are independent of the phases of all the other sinusoids.

Keywords:

Cramér-Rao bound; damped sinusoids; Fisher information matrix; close signals

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