A new transform for solving the noisy complex exponentials approximation problem

Details A new transform for solving the noisy complex exponentials approximation problem A new transform for solving the noisy complex exponentials approximation problem

2008-01-11

arxiv.org/abs/0801.1758v1

Journal of Approximation Theory, vol.155, pp. 1-27, 2008

Mathematics

Statistics Theory

42 pages, 5 figures

Scientific paper

10.1016/j.jat.2008.04.007

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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