A new transform for solving the noisy complex exponentials approximation problem

Authors:
P. Barone
Affiliations:
Istituto per le Applicazioni del Calcolo "M. Picone", C.N.R., Viale del Policlinico 137, 00161 Rome, Italy
Venue:
Journal of Approximation Theory
Year:
2008

Citing 11
Cited 5

Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions

Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
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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 computing an estimate of the unknown measure. A small simulation study is also performed to experimentally check the goodness of the approximations.