Aliasing effects for random fields over spheres of arbitrary dimension - Durastanti, Claudio; Patschkowski, Tim (Technische Universität Dortmund, 2018)
In 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.
Discussion Paper / SFB823;32/2018
Keywords: spherical random ﬁelds; band-limited random ﬁelds; aliasing function; aliases; hyperspherical harmonics; Gegenbauer polynomials; Gauss-Gegenbauer quadrature; harmonic analysis; 310; 330; 620