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. 2017 Aug 29;7:9651. doi: 10.1038/s41598-017-09884-w

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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A comparison of frequency-resolution capability of different methods. (a), (c), and (e) show the Fourier-transformed magnitude spectra of 600 noisy FID samples consisting of two frequencies separated by ΔF = 10 Hz and sampled at 12 kHz for S/N = 7.5; 10; 15, respectively. Figs (b), (d), and (f) show the corresponding zoomed-in plots together with the true frequencies (in blue), FRI-NMR estimates (in red), and LPSVD estimates (in cyan). FRI-NMR is able to resolve frequencies that are below the resolution limit (20 Hz) of the Fourier and Linear prediction method for different S/N levels.