Aliasing Effects for Samples of Spin Random Fields on the Sphere
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908782689255424 |
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| author | Durastanti, Claudio |
| author_facet | Durastanti, Claudio |
| contents | This paper investigates aliasing effects emerging from the reconstruction from discrete samples of spin spherical random fields defined on the two-dimensional sphere. We determine the location in the frequency domain and the intensity of the aliases of the harmonic coefficients in the Fourier decomposition of the spin random field and evaluate the consequences of aliasing errors in the angular power spectrum when the samples of the random field are obtained by using some very popular sampling procedures on the sphere, the equiangular and the Gauss-Jacobi sampling schemes. Finally, we demonstrate that band-limited spin random fields are free from aliases, provided that a sufficiently large number of nodes is used in the selected quadrature rule. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Aliasing Effects for Samples of Spin Random Fields on the Sphere Durastanti, Claudio Probability Statistics Theory 62M15, 62M40 This paper investigates aliasing effects emerging from the reconstruction from discrete samples of spin spherical random fields defined on the two-dimensional sphere. We determine the location in the frequency domain and the intensity of the aliases of the harmonic coefficients in the Fourier decomposition of the spin random field and evaluate the consequences of aliasing errors in the angular power spectrum when the samples of the random field are obtained by using some very popular sampling procedures on the sphere, the equiangular and the Gauss-Jacobi sampling schemes. Finally, we demonstrate that band-limited spin random fields are free from aliases, provided that a sufficiently large number of nodes is used in the selected quadrature rule. |
| title | Aliasing Effects for Samples of Spin Random Fields on the Sphere |
| topic | Probability Statistics Theory 62M15, 62M40 |
| url | https://arxiv.org/abs/2408.17078 |