Systematic and statistical uncertainties of the hilbert-transform based high-precision FID frequency extraction method

Hong, Ran; Corrodi, Simon; Charity, Saskia; Baeßler, Stefan; Bono, Jason; Chupp, Timothy; Fertl, Martin; Flay, David; García, Alejandro; George, Jimin; Giovanetti, Kevin Louis; Gorringe, Timothy; Grange, Joseph; Hong, Kyun Woo; Kawall, David; Kiburg, Brendan; Li, Bingzhi; Li, Liang; Osofsky, Rachel; Počanić, Dinko; Ramachandran, Suvarna; Smith, Matthias; Swanson, Herbert Erik; Tewsley-Booth, Alec; Winter, Peter; Yang, Tianyu; Zheng, Kai

doi:10.1016/j.jmr.2021.107020

Title: Systematic and statistical uncertainties of the hilbert-transform based high-precision FID frequency extraction method

Journal Article · Tue Jun 15 00:00:00 EDT 2021 · Journal of Magnetic Resonance

DOI:https://doi.org/10.1016/j.jmr.2021.107020· OSTI ID:1779484

Hong, Ran; Corrodi, Simon; Charity, Saskia; Baeßler, Stefan; Bono, Jason; Chupp, Timothy; Fertl, Martin; Flay, David; García, Alejandro; George, Jimin; Giovanetti, Kevin Louis; Gorringe, Timothy; Grange, Joseph; Hong, Kyun Woo; Kawall, David; Kiburg, Brendan; Li, Bingzhi; Li, Liang; Osofsky, Rachel; Počanić, Dinko more »

Pulsed nuclear magnetic resonance (NMR) is widely used in high-precision magnetic field measurements. The absolute value of the magnetic field is determined from the precession frequency of nuclear magnetic moments. The Hilbert transform is one of the methods that have been used to extract the phase function from the observed free induction decay (FID) signal and then its frequency. In this paper, a detailed implementation of a Hilbert-transform based FID frequency extraction method is described, and it is briefly compared with other commonly used frequency extraction methods. How artifacts and noise level in the FID signal affect the extracted phase function are derived analytically. A method of mitigating the artifacts in the extracted phase function of an FID is discussed. Correlations between noises of the phase function samples are studied for different noise spectra. We discovered that the error covariance matrix for the extracted phase function is nearly singular and improper for constructing the chi(2) used in the fitting routine. A down-sampling method for fixing the singular covariance matrix has been developed, so that the minimum chi(2)-fit yields properly the statistical uncertainty of the extracted frequency. Other practical methods of obtaining the statistical uncertainty are also discussed. (C) 2021 Elsevier Inc. All rights reserved.

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Research Organization:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); National Natural Science Foundation of China (NSFC)

Contributing Organization:: Muon g-2 Collaboration

Grant/Contract Number:: AC02-07CH11359; AC02-06CH11357

OSTI ID:: 1779484

Alternate ID(s):: OSTI ID: 1807594; OSTI ID: 1863245

Report Number(s):: FERMILAB-PUB-21-017-E; arXiv:2101.08412; oai:inspirehep.net:1842180; TRN: US2209659

Journal Information:: Journal of Magnetic Resonance, Vol. 329; ISSN 1090-7807

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (12)

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uncertainty analysis

Title: Systematic and statistical uncertainties of the hilbert-transform based high-precision FID frequency extraction method

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