Approximating with Gaussians

2008/05/25 by Craig Calcaterra, Calcaterra, Craig, Axel Boldt +1 · 1 citation
Computer Science · Engineering · Mathematics · #Control Systems and Identification #Digital Filter Design and Implementation #Numerical Methods and Algorithms #math.CA #math.FA #msc:41A30 #msc:42A32 #msc:42C10

paper · pdf · doi:10.48550/arxiv.0805.3795

16 pages, 23 figures

arxiv created 2008/05/25 · arxiv updated 2009/12/01

Abstract

Linear combinations of translations of a single Gaussian, e^-x2, are shown to be dense in L²(R). Two algorithms for determining the coefficients for the approximations are given, using orthogonal Hermite functions and least squares. Taking the Fourier transform of this result shows low-frequency trigonometric series are dense in L² with Gaussian weight function.

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