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NMR spectroscopy threshold signal-to-noise ratio

NMR-Spektroskopie Grenzwert des Signal-Rausch-Verhältnisses
  • Petar Kolar

    Petar Kolar was born in Koprivnica, Croatia in 1992. He received the B. S. degree in electrical engineering and information technology, the M. S. degree in information and communication technology, and the Ph. D. degree in the scientific field of electrical engineering from the Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia, in 2013, 2015 and 2020, respectively. From 2016 to 2019 he was a Research and Teaching Assistant with the Experimental Physics Division of the Department of Physics at the Faculty of Science, University of Zagreb, Zagreb, Croatia. Currently, he works as a Senior Instruments and Probes Development Associate with INETEC d.o.o., Lučko, Croatia. He is the author or co-author of three international journal papers and six conference papers. His research interests include computer programming, microwave and RF engineering, electronics, and embedded electronics.

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    , Lovro Blažok

    Lovro Blažok was born in Koprivnica, Croatia in 1994. He received the B. S. degree in geological engineering and the M. S. degree in geological engineering from the Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Zagreb, Croatia in 2016 and 2018, respectively. From 2018 to 2020 he was a Geological Engineer/Hydro-geologist with FIL.B.IS. projekt d.o.o., Zagreb, Croatia. Since 2020 he is working as a Geological Engineer with Geotech d.o.o., Rijeka, Croatia. He participated in two international journal papers and two conference papers as a co-author. His research interests include computer programming, geological engineering, hydro-geology and drilling.

    and Dario Bojanjac

    Dario Bojanjac was born in Zagreb, Croatia in 1986. He received dipl. ing. and Ph. D. degree in electrical engineering from the Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia, in 2009 and 2015 respectively and B. S. degree in mathematics from the Faculty of Science, University of Zagreb. From 2009 to 2019 he was a Research and Teaching Assistant at the Department of Wireless Communications, Faculty of Electrical Engineering and Computing, University of Zagreb. Since 2019 he is Assistant Professor at the same department. He is the author or co-author of 5 international journal papers and 8 conference papers. His research interests include numerical methods for Maxwell’s equations, mathematical modelling of electromagnetic scattering problems and homogenization techniques for PDEs.

From the journal tm - Technisches Messen

Abstract

Ever since noise was spotted and proven to cause problems for the transmission and detection of information through a communication channel, a standard procedure in the process of characterizing a detection system of the communication channel is to determine the level of the lowest detectable signal. In signal processing, this is usually done by determining the so-called threshold signal-to-noise ratio (SNR). This determination is especially important for the communication channels and systems that constantly operate with low-level signals. A good example of such a system is definitely the NMR spectroscopy system. However, to the authors’ knowledge, the threshold SNR value of NMR spectroscopy systems has not been determined yet. That is why the experts in the field of NMR spectroscopy were asked to assess, using an online questionnaire, which SNR level they considered to be the NMR threshold SNR level. Afterwards, the threshold value was calculated from the obtained data. Finally, it was compared to the existing rule of thumb and thus, a conclusion about its legitimacy was made. The described questionnaire is still available online (https://forms.gle/Y9hyDZ1v1iJoEbk27). This enables everyone to form their own opinion about the threshold SNR level, which the authors encourage the readers to do.

Zusammenfassung

Seitdem erkannt und bewiesen wurde, dass Rauschen bei der Übertragung und Detektion von Informationen über einen Kommunikationskanal Probleme verursacht, ist es Standard, den niedrigsten Signalpegel anzugeben, der detektiert werden kann. Dieser charakterisiert die Empfangseinheit des Kanals. In der Signalverarbeitung wird dieser Grenzwert für gewöhnlich in Form des Signal-zu-Rausch-Verhältnisses, angelsächsisch signal-to-noise ratio (SNR), angegeben. Die Bestimmung dieses Wertes ist besonders wichtig für Systeme, die permanent bei einem niedrigen Signalpegel arbeiten. Ein gutes Beispiel für solch ein System ist die NMR-Spektroskopie. Nach dem Wissen der Autoren wurde dieses Signal-zu-Rausch-Verhältnis für die NMR-Spektroskopie jedoch bisher nicht bestimmt. Aus diesem Grund wurden Experten auf dem Gebiet der NMR-Spektroskopie via Online-Fragebogen gebeten, anzugeben, ihre Meinung zu äußern, welchen Wert der (Grenzwert/Schwellenwert) für dieses Verhältnis hat. Im Anschluss werde der Grenzwert basierend auf den erhaltenen Daten berechnet. Darüber hinaus wurden Schlussfolgerungen über die Herkunft und Legitimität der Werte gezogen, indem sie mit der bestehenden Faustregel verglichen wurden. Der oben erwähnte Online-Fragebogen steht weiterhin im Netz zur Verfügung (https://forms.gle/Y9hyDZ1v1iJoEbk27). Dies ermöglicht jedem, sich eine eigene Meinung über ihn zu bilden, wozu die Autoren herzlich einladen.

About the authors

Petar Kolar

Petar Kolar was born in Koprivnica, Croatia in 1992. He received the B. S. degree in electrical engineering and information technology, the M. S. degree in information and communication technology, and the Ph. D. degree in the scientific field of electrical engineering from the Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia, in 2013, 2015 and 2020, respectively. From 2016 to 2019 he was a Research and Teaching Assistant with the Experimental Physics Division of the Department of Physics at the Faculty of Science, University of Zagreb, Zagreb, Croatia. Currently, he works as a Senior Instruments and Probes Development Associate with INETEC d.o.o., Lučko, Croatia. He is the author or co-author of three international journal papers and six conference papers. His research interests include computer programming, microwave and RF engineering, electronics, and embedded electronics.

Lovro Blažok

Lovro Blažok was born in Koprivnica, Croatia in 1994. He received the B. S. degree in geological engineering and the M. S. degree in geological engineering from the Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Zagreb, Croatia in 2016 and 2018, respectively. From 2018 to 2020 he was a Geological Engineer/Hydro-geologist with FIL.B.IS. projekt d.o.o., Zagreb, Croatia. Since 2020 he is working as a Geological Engineer with Geotech d.o.o., Rijeka, Croatia. He participated in two international journal papers and two conference papers as a co-author. His research interests include computer programming, geological engineering, hydro-geology and drilling.

Dario Bojanjac

Dario Bojanjac was born in Zagreb, Croatia in 1986. He received dipl. ing. and Ph. D. degree in electrical engineering from the Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia, in 2009 and 2015 respectively and B. S. degree in mathematics from the Faculty of Science, University of Zagreb. From 2009 to 2019 he was a Research and Teaching Assistant at the Department of Wireless Communications, Faculty of Electrical Engineering and Computing, University of Zagreb. Since 2019 he is Assistant Professor at the same department. He is the author or co-author of 5 international journal papers and 8 conference papers. His research interests include numerical methods for Maxwell’s equations, mathematical modelling of electromagnetic scattering problems and homogenization techniques for PDEs.

Acknowledgment

This contribution was revised by Klara Kolar, mag. philol. ang. et russ. The translation to German language was done by Dipl.-Ing. Björn Neubauer.

Figure 4 
NMR spectroscopy threshold SNR integrated into the NMR spectroscopy online calculator: the predicted signal’s SNR is lower than the threshold SNR.
Figure 4

NMR spectroscopy threshold SNR integrated into the NMR spectroscopy online calculator: the predicted signal’s SNR is lower than the threshold SNR.

Figure 5 
NMR spectroscopy threshold SNR integrated into the NMR spectroscopy online calculator: the predicted signal’s SNR is equal to the threshold SNR.
Figure 5

NMR spectroscopy threshold SNR integrated into the NMR spectroscopy online calculator: the predicted signal’s SNR is equal to the threshold SNR.

Figure 6 
The relation between the signal level and its respective noise level (signal-to-noise ratio definition).
Figure 6

The relation between the signal level and its respective noise level (signal-to-noise ratio definition).

Appendix A Integration of the NMR threshold SNR into the NMR spectroscopy online calculator

Recently, a simple, but accurate, noise model of the NMR spectroscopy receiving chain has been introduced [9], [21]. The primary function of this model is to a priori analyze and optimize the used NMR spectroscopy system and, in the end, either enable the measurement of NMR samples with response signals lower than the ones that are measured today, or reduce the modern NMR samples’ overall measurement duration [22]. The model was “forged” into a simple Javascript-based calculator which is made available online [23].

The latest feature added to the calculator is the integration of the NMR spectroscopy threshold SNR, presented in this contribution, with the calculator. In addition to the SNR prediction of the NMR signal, shown on the spectrometer screen, the calculator now also informs its user whether or not the predicted NMR signal is detectable, according to the NMR spectroscopy threshold SNR. The end results of the calculator’s usage in the case when the predicted NMR signal’s SNR is lower than the NMR threshold SNR, and in the case when the predicted NMR signal’s SNR is greater than or equal to the NMR threshold SNR, can be seen in Figures 4 and 5, respectively.

Figure 7
Figure 7
Figure 7

Appendix B A text copy of the entire Google Form online questionnaire

Determination of “the worst good” NMR signal

Below, you can see a range of signals, generated with MATLAB, whose signal-to-noise ratios (SNRs) span from −6 dB (which is equal to the ratio of 0.5 in the voltage scale) to 33 dB (the ratio of 45 in the voltage scale), arranged from the lowest to the highest SNR value.

These signals’ background noises have equal root mean square (RMS) values, whereas their signal values change. In order to make signal comparison as easy as possible, all the signals’ charts have the same axes scales.

The only thing that needs to be taken into consideration here is the relation between the signal level and its respective noise level (see Figure 6). What you choose here is the signal with the worst (that is, the smallest) difference between its magnitude and its background noise which you consider good enough to be presented as a satisfactory result of an NMR measurement.

Without further ado, here is the question: Of all the signals shown in Figure 7, which is the first one that you consider satisfactory enough to be presented as a good NMR measurement result? (For a better preview, images of better resolution are available here: https://flic.kr/s/aHsmPd16X1.)

References

1. C.D. Richmond, Capon algorithm mean-squared error threshold SNR prediction and probability of resolution, IEEE Transactions on Signal Processing 53 (8) (2005) 2748–2764. doi:10.1109/TSP.2005.850361.Search in Google Scholar

2. C.D. Motchenbacher and J.A. Connelly, Low-Noise Electronic System Design, John Wiley & Sons, Inc., USA, 1993.Search in Google Scholar

3. A. Abragam, The Principles of Nuclear Magnetism, Oxford University Press, UK, 1961.10.1063/1.3057238Search in Google Scholar

4. E. Fukushima and S.B.W. Roeder, Experimental Pulse NMR: A Nuts and Bolts Approach, Addition-Wesley Publishing Company, USA, 1981.Search in Google Scholar

5. R. Tandra and A. Sahai, SNR Walls for Signal Detection, IEEE Journal of Selected Topics in Signal Processing 2 (1) (2008) 4–17. doi:10.1109/JSTSP.2007.914879.Search in Google Scholar

6. I.R. Kleckner and M.P. Foster, An introduction to NMR-based approaches for measuring protein dynamics, Biochimica et Biophysica Acta (BBA) – Proteins and Proteomics 1814 (8) (2011) 942–968. doi:10.1016/j.bbapap.2010.10.012.Search in Google Scholar PubMed PubMed Central

7. A.M. Torres and W.S.Price, Common problems and artifacts encountered in solution-state NMR experiments, Concepts in Magnetic Resonance: Part A 45A (2) (2017) e21387. doi:10.1002/cmr.a.21387.Search in Google Scholar

8. A. Webb, Increasing the Sensitivity of Magnetic Resonance Spectroscopy and Imaging, Analytical Chemistry 84 (1) (2011) 9–16. doi:10.1021/ac201500v.Search in Google Scholar PubMed

9. P. Kolar, M.S. Grbić and S. Hrabar, Sensitivity Enhancement of NMR Spectroscopy Receiving Chain Used in Condensed Matter Physics, Sensors 19 (14) (2019) 3064. doi:10.3390/s19143064.Search in Google Scholar PubMed PubMed Central

10. S.G. Hyberts and S.A. Robson, Exploring signal-to-noise ratio and sensitivity in non-uniformly sampled multi-dimensional NMR spectra, Journal of Biomolecular NMR 55 (2012) 167–178. doi:10.1007/s10858-012-9698-2.Search in Google Scholar PubMed PubMed Central

11. B. Simon and H. Köstler, Improving the sensitivity of FT-NMR spectroscopy by apodization weighted sampling, Journal of Biomolecular NMR 73 (2019) 155–165. doi:10.1007/s10858-019-00243-7.Search in Google Scholar PubMed PubMed Central

12. A. Rahman, M.I. Choudhary and A. Wahab, Solving Problems with NMR Spectroscopy, 2nd Edition, Elsevier Academic Press, USA, 2016.Search in Google Scholar

13. P. Kolar, Determination of “the worst good” NMR signal, https://forms.gle/ZLcqLRDmZwwrjLnP9, Google Forms (2020).Search in Google Scholar

14. D.M. Pozar, Microwave Engineering, 4th Edition, John Wiley & Sons, Inc., USA, 2011.Search in Google Scholar

15. S.S. Stevens, On the Theory of Scales of Measurement, Science 103 (2684) (1946) 677–680. doi:10.1126/science.103.2684.677.Search in Google Scholar PubMed

16. S.S. Stevens, On the Averaging of Data, Science 121 (3135) (1955) 113–116. doi:10.1126/science.121.3135.113.Search in Google Scholar PubMed

17. M. Hiebel, Fundamentals of Vector Network Analysis, 6th Edition, Rohde & Schwarz, Germany, 2014.Search in Google Scholar

18. A. Rose, The Sensitivity Performance of the Human Eye on an Absolute Scale, Journal of the Optical Society of America 38 (2) (1948) 196–208. doi:10.1364/JOSA.38.000196.Search in Google Scholar

19. U. Sharma and N.R. Jagannathan, Breast Magnetic Resonance Spectroscopy (MRS), American Cancer Society, 2009. doi:10.1002/9780470034590.emrstm1167.Search in Google Scholar

20. J.G. Kereikas, S.R. Thomas and C.G. Orton (Ed.), Digital Radiography, 1st Edition, Plenum Press, USA, 1986.10.1007/978-1-4684-5068-2Search in Google Scholar

21. P. Kolar, L. Blažok and D. Bojanjac, How (and why) to determine NMR spectrometer’s noise figure? tm – Technisches Messen 87 (10) (2020) 614–621. doi:10.1515/teme-2020-0043.Search in Google Scholar

22. P. Kolar, Optimization of radio frequency components of cryogenic Nuclear Magnetic Resonance spectroscopy system, Ph.D. thesis, University of Zagreb, Croatia 2020.Search in Google Scholar

23. P. Kolar, L. Blažok and D. Bojanjac, NMRCalc: NMR Spectroscopy Rx Chain Noise Figure Calculator, https://nmrcalc.github.io/, Interactive website via GitHub (2020).Search in Google Scholar

Received: 2021-02-04
Accepted: 2021-04-06
Published Online: 2021-04-17
Published in Print: 2021-09-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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