{"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/a-complete-framework-for-linear-filtering-of","title":"A complete framework for linear filtering of bivariate signals","arxiv_id":"1802.02469","date":"2018-02-07","proceeding":null,"authors":["Julien Flamant","Pierre Chainais","Nicolas Le Bihan"],"abstract":"A complete framework for the linear time-invariant (LTI) filtering theory of\nbivariate signals is proposed based on a tailored quaternion Fourier transform.\nThis framework features a direct description of LTI filters in terms of their\neigenproperties enabling compact calculus and physically interpretable\nfiltering relations in the frequency domain. The design of filters exhibiting\nfondamental properties of polarization optics (birefringence, diattenuation) is\nstraightforward. It yields an efficient spectral synthesis method and new\ninsights on Wiener filtering for bivariate signals with prescribed\nfrequency-dependent polarization properties. This generic framework facilitates\noriginal descriptions of bivariate signals in two components with specific\ngeometric or statistical properties. Numerical experiments support our\ntheoretical analysis and illustrate the relevance of the approach on synthetic\ndata.","url_abs":"http://arxiv.org/abs/1802.02469v1","url_pdf":"http://arxiv.org/pdf/1802.02469v1.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":"a-complete-framework-for-linear-filtering-of","repo_url":"https://github.com/jflamant/bispy","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}