{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/harmonic-analysis-of-isotropic-fields-on-the","title":"Harmonic analysis of isotropic fields on the sphere with arbitrary masks","arxiv_id":"2109.13352","date":"2021-09-27","proceeding":null,"authors":["Henry S. Grasshorn Gebhardt","Olivier Doré"],"abstract":"Obtaining constraints from the largest scales of a galaxy survey is challenging due to the survey mask allowing only partial measurement of large angular modes. This scatters information from the harmonic-space 2-point function away from the diagonal and introduces coupling between modes. In this paper, we derive a custom eigenbasis adapted to any particular survey geometry so that all information is retained on the diagonal. At the expense of a somewhat complex pixel- and selection-function-window, the result is a diagonal 2-point function with a simple shot noise, and a diagonal covariance matrix in the case of a Gaussian random field. We derive the basis on the surface of a sphere, and we use it to construct a 3D spherical Fourier-Bessel power spectrum estimator assuming a survey geometry that is separable in the angular and radial directions.","url_abs":"https://arxiv.org/abs/2109.13352v2","url_pdf":"https://arxiv.org/pdf/2109.13352v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"harmonic-analysis-of-isotropic-fields-on-the","repo_url":"https://github.com/hsgg/cryofabs.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}