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 computing in estimate of the Unknown measure. A small simulation study is also performed to experimentally check, the goodness of the approximations.
A new transform for solving the noisy complex exponentials approximation problem
Barone P
2008
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 computing in estimate of the Unknown measure. A small simulation study is also performed to experimentally check, the goodness of the approximations.File in questo prodotto:
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