{"paper":{"title":"Accuracy of Algebraic Fourier Reconstruction for Shifts of Several Signals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dmitry Batenkov, Niv Sarig, Yosef Yomdin","submitted_at":"2013-11-14T11:42:40Z","abstract_excerpt":"We consider the problem of \"algebraic reconstruction\" of linear combinations of shifts of several known signals $f_1,\\ldots,f_k$ from the Fourier samples. Following \\cite{Bat.Sar.Yom2}, for each $j=1,\\ldots,k$ we choose sampling set $S_j$ to be a subset of the common set of zeroes of the Fourier transforms ${\\cal F}(f_\\ell), \\ \\ell \\ne j$, on which ${\\cal F}(f_j)\\ne 0$. It was shown in \\cite{Bat.Sar.Yom2} that in this way the reconstruction system is \"decoupled\" into $k$ separate systems, each including only one of the signals $f_j$. The resulting systems are of a \"generalized Prony\" form.\n  H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3468","kind":"arxiv","version":2},"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"}