A new transform for solving the noisy complex exponentials approximation problem

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.

42 pages, 5 figures

References in corpus (3)

• A new transform for solving the noisy complex exponentials approximation problem
• On the condensed density of the generalized eigenvalues of pencils of Hankel Gaussian random matrices and applications
• Computational aspects and applications of a new transform for solving the complex exponentials approximation problem

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