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oai:drops-oai.dagstuhl.de:10612 2024-03-06T10:46:16Z ddc:004 open_access

Estimating the Frequency of a Clustered Signal Chen, Xue Price, Eric sublinear algorithms Fourier transform 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 + O~(k^3) from samples on [-1, 1]. This improves upon the best previous bound of O(Delta + O~(k^5))^{1.5}. We also show that no algorithm can do better than Delta + O~(k^2). In the process we provide a new O~(k^3) bound on the ratio between the maximum and average value of continuous k-Fourier-sparse signals, which has independent application. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Xue Chen and Eric Price 2019 Is Part Of LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2019.36 urn:nbn:de:0030-drops-106128 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.36 eng https://creativecommons.org/licenses/by/3.0/legalcode