Aliasing effects for random fields over spheres of arbitrary dimension

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dc.contributor.authorDurastanti, Claudio
dc.contributor.authorPatschkowski, Tim
dc.date.accessioned2018-12-04T08:32:55Z
dc.date.available2018-12-04T08:32:55Z
dc.date.issued2018
dc.description.abstractIn this paper, aliasing effects are investigated for random fields defined on the d-dimensional sphere Sd, and reconstructed from discrete samples. First, we introduce the concept of an aliasing function on Sd. The aliasing function allows to identify explicitly the aliases of a given harmonic coefficient in the Fourier decomposition. Then, we exploit this tool to establish the aliases of the harmonic coefficients approximated by means of the quadrature procedure named spherical uniform sampling. Subsequently, we study the consequences of the aliasing errors in the approximation of the angular power spectrum of an isotropic random field, the harmonic decomposition of its covariance function. Finally, we show that band- limited random fields are aliases-free, under the assumption of a sufficiently large amount of nodes in the quadrature rule.en
dc.identifier.urihttp://hdl.handle.net/2003/37827
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-19822
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB823;32/2018en
dc.subjectspherical random fieldsen
dc.subjectband-limited random fieldsen
dc.subjectaliasing functionen
dc.subjectaliasesen
dc.subjecthyperspherical harmonicsen
dc.subjectGegenbauer polynomialsen
dc.subjectGauss-Gegenbauer quadratureen
dc.subjectharmonic analysisen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleAliasing effects for random fields over spheres of arbitrary dimensionen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access
eldorado.secondarypublicationfalsede

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