{"paper":{"title":"Estimating the Frequency of a Clustered Signal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Eric Price, Xue Chen","submitted_at":"2019-04-30T04:08:40Z","abstract_excerpt":"We consider the problem of locating a signal whose frequencies are \"off grid\" and clustered in a narrow band. Given noisy sample access to a function $g(t)$ with Fourier spectrum in a narrow range $[f_0 - \\Delta, f_0 + \\Delta]$, how accurately is it possible to identify $f_0$? We present generic conditions on $g$ that allow for efficient, accurate estimates of the frequency. We then show bounds on these conditions for $k$-Fourier-sparse signals that imply recovery of $f_0$ to within $\\Delta + \\tilde{O}(k^3)$ from samples on $[-1, 1]$. This improves upon the best previous bound of $O\\big( \\Delt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.13043","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"}