Aliasing effects for random fields over spheres of arbitrary dimension

Abstract

In this paper, aliasing effects are investigated for random fields defined on the d-dimensional sphere and reconstructed from discrete samples. First, we introduce the concept of an aliasing function on the sphere. The aliasing function allows one 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.

arXiv comment39 pages, 2 figures

References in corpus (10)

• A novel sampling theorem on the sphere
• Isotropic Gaussian random fields on the sphere: Regularity, fast simulation and stochastic partial differential equations
• Asymptotics for spherical needlets
• Exact Wavelets on the Ball
• High-resolution asymptotics for the angular bispectrum of spherical random fields
• Subsampling needlet coefficients on the sphere
• Optimal designs for three-dimensional shape analysis with spherical harmonic descriptors
• A Simple Proposal for Radial 3D Needlets
• Ergodicity and Gaussianity for Spherical Random Fields
• Gaussian semiparametric estimates on the unit sphere