{"paper":{"title":"Decoupling of Fourier Reconstruction System 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":"2013-05-13T16:22:13Z","abstract_excerpt":"We consider the problem of ``algebraic reconstruction'' of linear combinations of shifts of several signals $f_1,\\ldots,f_k$ from the Fourier samples. For each $r=1,\\ldots,k$ we choose sampling set $S_r$ to be a subset of the common set of zeroes of the Fourier transforms ${\\cal F}(f_\\l), \\ \\l \\ne r$, on which ${\\cal F}(f_r)\\ne 0$. We show that in this way the reconstruction system is reduced to $k$ separate systems, each including only one of the signals $f_r$. Each of the resulting systems is of a ``generalized Prony'' form. We discuss the problem of unique solvability of such systems, and p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2832","kind":"arxiv","version":1},"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"}