{"paper":{"title":"Analytic signal in many dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CV","math.IT","math.SP"],"primary_cat":"eess.SP","authors_text":"Mikhail Tsitsvero, Paulo Gon\\c{c}alves, Pierre Borgnat","submitted_at":"2017-12-25T16:32:15Z","abstract_excerpt":"In this work we extend analytic signal theory to the multidimensional case when oscillations are observed in the $d$ orthogonal directions. First it is shown how to obtain separate phase-shifted components and how to combine them into instantaneous amplitude and phases. Second, the proper hypercomplex analytic signal is defined as holomorphic hypercomplex function on the boundary of certain upper half-space. Next it is shown that correct phase-shifted components can be obtained by positive frequency restriction of hypercomplex Fourier transform. Necessary and sufficient conditions for analytic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09350","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}