{"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/spectral-derivatives","title":"Spectral Derivatives","arxiv_id":"2506.06210","date":"2025-06-06","proceeding":null,"authors":["Pavel Komarov"],"abstract":"One of the happiest accidents in all math is the ease of transforming a function to and taking derivatives in the Fourier frequency domain. But in order to exploit this extraordinary fact without serious artefacting, and in order to be able to use a computer, we need quite a bit of extra knowledge and care. This document sets out the math behind the spectral-derivatives Python package. I touch on fundamental signal processing and calculus concepts as necessary and build upwards.","url_abs":"https://arxiv.org/abs/2506.06210v2","url_pdf":"https://arxiv.org/pdf/2506.06210v2.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":"abstracts"},"code_links":[{"paper_slug":"spectral-derivatives","repo_url":"https://github.com/pavelkomarov/spectral-derivatives","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"jax","reach":null}],"tasks":[{"task_slug":"math","task_name":"Math"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}