A new transform for solving the noisy complex exponentials approximation problem

Piero Barone

doi:10.1016/j.jat.2008.04.007

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arXiv · 0801.1758

A new transform for solving the noisy complex exponentials approximation problem

Piero Barone

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Abstract

The problem of estimating a complex measure made up by a linear combination of Dirac distributions centered on points of the complex plane from a finite number of its complex moments affected by additive i.i.d. Gaussian noise is considered. A random measure is defined whose expectation approximates the unknown measure under suitable conditions. An estimator of the approximating measure is then proposed as well as a new discrete transform of the noisy moments that allows to compute an estimate of the unknown measure. A small simulation study is also performed to experimentally check the goodness of the approximations.

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Piero Barone. 2008-01-11. A new transform for solving the noisy complex exponentials approximation problem. https://doi.org/10.1016/j.jat.2008.04.007

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