eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-07-04
36:1
36:13
10.4230/LIPIcs.ICALP.2019.36
article
Estimating the Frequency of a Clustered Signal
Chen, Xue
1
Price, Eric
2
Northwestern University, Evanston, IL, USA
The University of Texas at Austin, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol132-icalp2019/LIPIcs.ICALP.2019.36/LIPIcs.ICALP.2019.36.pdf
sublinear algorithms
Fourier transform