CC BY
3
i i St. Petersburg Polytechnic University Journal: Physics and Mathematics. 2022 Vol. 15, No. 3.2 Научно-технические ведомости СПбГПУ. Физико-математические науки. 15 (3.2) 2022
Conference materials UDC 543.4
DOI: https://doi.org/10.18721/JPM.153.264
Method for constructing NMR signal spectra using the discrete Fourier transform
S. S. Makeev
1 Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia
H st_makeev@mail.ru
Abstract. The article deals with studies of the structure of the nuclear magnetic resonance signal, which is recorded using the modulation technique. The influence of the properties of the medium on the possibility of registering an NMR signal in a weak magnetic field using a modulation technique for measuring is established. A new method for describing the registered NMR signal using the modulation technique is proposed, taking into account the contributions of absorption and dispersion signals. The features of the use of spectral analysis in the study of the NMR signal from liquid media are determined. The results of theoretical calculation and experimental studies are compared.
Keywords: condensed medium, nuclear magnetic resonance, amplitude spectrum, phase spectrum, absorption signal, dispersion signal
Citation: Makeev S. S., Method for constructing NMR signal spectra using the discrete Fourier transform, St. Petersburg State Polytechnical University Journal. Physics and Mathematics. 15 (3.2) (2022) 346-351. DOI: https://doi.org/10.18721/JPM.153.264
This is an open access article under the CC BY-NC 4.0 license (https://creativecommons. org/licenses/by-nc/4.0/)
Материалы конференции УДК 543.4
DOI: https://doi.org/10.18721/JPM.153.264
Методика построения спектров сигнала ЯМР с использованием дискретного преобразования Фурье
С. С. Макеев ,е
1 Санкт-Петербургский политехнический университет Петра Великого, Санкт-Петербург, Россия
н st_makeev@mail.ru
Аннотация. В статье рассмотрены исследования структуры сигнала ядерного магнитного резонанса, который регистрируется с помощью модуляционной методики. Установлено влияние свойств среды на возможности регистрации сигнала ЯМР в слабом магнитном поле с использованием модуляционной методики для проведения измерения. Предложена новая методика описания регистрируемого сигнала ЯМР с использованием модуляционный методики с учетом вкладов сигналов поглощения и дисперсии. Определены особенности использования спектрального анализа при исследовании сигнала ЯМР от жидких сред. Проведено сравнение результатов теоретического расчета и экспериментальных исследований.
Ключевые слова: конденсированная среда, ядерный магнитный резонанс, амплитудный спектр, фазовый спектр, сигнал поглощения, сигнал дисперсии
Ссылка при цитировании: Макеев С. С. Методика построения спектров сигнала ЯМР с использованием дискретного преобразования Фурье // Научно-технические ведомости СПбГПУ. Физико-математические науки. Т. 15. № 3.2. С. 346-351. DOI: https://doi. org/10.18721/JPM.153.264
Статья открытого доступа, распространяемая по лицензии CC BY-NC 4.0 (https:// creativecommons.org/licenses/by-nc/4.0/)
© Makeev S. S., 2022. Published by Peter the Great St. Petersburg Polytechnic University.
Introduction
The deterioration of the environment and the emergence of various negative factors for various reasons led to a decrease in the quality of liquid media [1—8]. Therefore, when conducting various experiments, manufacturing products, environmental control of hard-to-reach reservoirs and water protection zones, means of express control become extremely in demand [8—14]. In recent years, the division of this control into two parts which are control tools that conduct research in express mode (located in small stationary and mobile laboratories, require electrical power from the network) [15—18]. Measuring instruments that can be moved around the territory are battery-operated and allow obtaining information about the state of the environment at the sampling site [8, 19—21]. In these cases, new tasks arise that are associated with obtaining new information about the state of the environment from the data obtained during express control. One of these problems is considered in our work.
Method of nuclear magnetic resonance for express control and formation of the spectrum of NMR signals
The main condition for a qualitative study of liquid media is the preservation of their physical structure and chemical composition of the medium under study [21—24]. The fulfillment of this condition in the express control of any liquid can be achieved only with the help of devices whose operation is based on the phenomenon of nuclear magnetic resonance (NMR) [21—26]. Other types of devices for express control of the state of a liquid, such as optical, ultrasonic and X-ray devices, can fulfill this condition only when they work with a certain class of media [27—29].
The modulation technique is used to register the NMR signal in weak magnetic fields. The registered NMR signal in this case is obtained in the form of damped oscillations [8, 19, 26, 30, 31]. Using the shape of this signal, one can measure the relaxation constants T1 and T2 and determine the state of the medium [8, 19, 26, 30, 31]. When solving a number of problems, more information is required. To obtain it, we propose methods for processing NMR signals using spectral analysis.
One of the features of the application of spectral analysis is that the registered NMR signal is a non-periodic oscillation in the form of damped peaks. Therefore, it is advisable to use the discrete Fourier transform to describe the signal G(t), as well as the calculated absorption and dispersion signals:
N-1
xne-j 2nkn/N, (1)
n=0
where n = 0, 1, 2, ..., N—1; xn is the input data sequence; N is the number of elements of the input data sequence xn.
The harmonics of the spectrum are located on the frequency axis with a discreteness Af = f/N, where f is the sampling frequency of the initial sequence x. The sampling rate is determined as follows. Let t be the duration of the NMR signal. Then f can be calculated using the following relation:
f =N/T, (2)
In addition, when N is a power of two, the DFT is calculated by the FFT (Fast Fourier Transform) algorithm. It requires less computing resources and is much faster than the discrete Fourier transform. The DFT is symmetrical about the Nyquist frequency, which is equal to f/2, so harmonics with numbers (N/2—k) and (N/2+k) can be combined. The result is a one-sided complex spectrum with frequencies from 0 to f/2, which corresponds to indices k = 0...(N/2-1).
The scaled one-sided complex spectrum of the discrete input sequence xn is given by:
' >o k = 0
Ук =Ё
Ук =
V2 Ук- к = 1,2,
N
N -1 2
(3)
In relation (3), the operation in brackets [N/2—1] represents rounding to the nearest whole number. In this case, the amplitude spectrum S is equal to the modulus of the one-sided complex spectrum and the phase spectrum P(f) = argyk is its argument, where f = kAf
© Макеев С. С., 2022. Издатель: Санкт-Петербургский политехнический университет Петра Великого.
Comparison of the technique for forming the spectrum of NMR signals with the results of the experiment
To obtain information about the contribution of absorption and dispersion signals to the registered NMR signals, it is necessary to calculate the values of w(t) and u(t). Fig. 1 shows the calculated dependences w(t), u(t) and G(t) for oil.
An analysis of the received signals shows the absence of a period at the location of the decaying peaks, which makes it possible to use the DFT to calculate the spectra. For absorption and dispersion signals, the amplitude and phase spectra are calculated (Figs. 2 and 3).
T2* = 144 ms is calculated and NMR signal spectra for oil are plotted using (1)—(3). Fig. 4 shows the amplitude and phase spectra of the NMR signal for oil.
a)
b)
c)
A a ;
i \iiM/vwH } v u
A
a ■ \
\ I y V
I A
1 ! yVww^
Fig. 1. Calculation forms of NMR signals from oil: absorption (a); dispersion (b); sum signal G(t) (c)
a) b)
0.45 0.4 0 35
Q.3
go.a
S
I 112
0 15
mtÜM
-sa .15 -ta
f. Tu
ro 15 BS
Fig. 2. Amplitude spectra from the calculated NMR signal for oil: absorption (a); dispersion (b) a) b)
Fig. 3. Phase spectra from the calculated NMR signal for oil: absorption (a); dispersion (b)
Fig. 4. Spectra from calculated NMR signal for oil: amplitude (a); phase (b)
The obtained results show that the spectral components of the amplitude and phase spectrum can be expressed in terms of the spectral components of the amplitude and phase spectra of the signals v(t) and u(t). The coefficients that determine this relationship will be the contribution of these signals to the recorded NMR signal.
To test our proposed method, experimental studies of liquid media were carried out. With the help of the Matlab package, the amplitude and phase spectra of the NMR signals recorded from the oil sample were constructed, obtained using relations (1)—(3). Fig. 5 shows the spectra of the experimental NMR signal for oil.
a)
b)
a 0 «
-1 -2 -3
-4 -
0
f, ru
Fig. 5. Spectra from experimental NMR signal for oil: amplitude (a); phase (b)
Analysis of the presented spectra in Fig. 5 shows that the method proposed by us for modeling the spectra of NMR signals makes it possible to obtain good agreement between the theoretical and experimental data. This allows it to be used for effective express control of condensed media.
Having made similar calculations, T2* = 360 ms for kerosene and T2* = 440 ms for gasoline were obtained and the amplitude and phase spectra were plotted from the calculated NMR signals for kerosene and gasoline.
Further, using the Matlab package, the amplitude and phase spectra of NMR signals for kerosene and gasoline were constructed, obtained using relations (1)—(3). Figs. 6 and 7 show the spectra of the experimental NMR signal for kerosene and gasoline.
It should be noted that the registration of the NMR signal in a weak field is carried out at the maximum signal-to-noise ratio of the signal. In this case, the absorption signal is always greater than the signal dispersion, the coefficients are uniquely determined. In the study of such mixtures, the number of coefficients increases, and coefficients appear corresponding to the concentrations of media in the mixture. Their determination makes it possible to determine the composition and concentration of the components in the mixture.
Fig. 6. Amplitude spectra from the experimental NMR signal: kerosene (a); gasoline (b)
a) b)
Fig. 7. Phase spectra from the experimental NMR signal: kerosene (a); gasoline (b)
Conclusion
As a result, it was found that the proposed spectral research method has no restrictions on its use. To use it, it is necessary to register the NMR signal from a medium containing nuclei with magnetic moments, for example, at the resonant frequency of protons (more than 99% of liquid media contain protons) and measure the relaxation constants T1 and T2 to calculate absorption and dispersion signals.
REFERENCES
1. Mazing M. S., Zaitceva A. Yu., Kislyakov Yu. Ya., Kondakov N. S., Avdushenko S. A., Davydov
V. V., Monitoring of Oxygen Supply of Human Tissues Using A Noninvasive Optical System Based on A MultiChannel Integrated Spectrum Analyzer, International Journal of Pharmaceutical Research. 12(2) (2020) 1974-1978.
2. Kislyakov Yu. Ya., Avdyushenko S. A., Kislyakova I. P., Zaitceva A. Yu., Analytical multisensory trainable system for diagnosing vocational aptitude of military medical specialists by ion content in the expired breath conden sate, Journal of Computational and Theoretical Nanos cience. 16(11) (2019) 4502-4507.
3. Gryaznova E. M., Rud V. Y., On the possibility of using the optical method for express quality control of fruits, Journal of Physics: Conference Series 2086(1) (2021) 012143.
4. Davydov R. V., Yushkova V. V., Stirmanov A. V., Rud V. Yu., A new method for monitoring the health condition based on nondestructive signals of laser radiation absorption and scattering, Journal of Physics: Conference Series. 1410(1) (2019) 012067.
5. Davydov, V. V., Myazin, N. S., Grebenikova, N. M., & Dudkin, V. I., Determination of the Composition and Concentrations of the Components of Mixtures of Hydrocarbon Media in the Course of its Express Analysis. Measurement Techniques, 62(12), 1090-1098.
6. Grebenikova N. M., Smirnov K. J., Rud V. Yu., Artemiev V. V., Features of monitoring the state of the liquid medium by refractometer, Journal of Physics: Conference Series. 1135(1) (2018) 012055.
7. Grebenikova N. M., Smirnov K. J., Features of optical signals processing for monitoring the state of the flowing liquid medium with a refractometer, Journal of Physics: Conference Series. 1368(2) (2019) 022057.
8. Davydov V. V., Davydova T. I., A nondestructive method for express testing of condensed media in ecological monitoring, Russian Journal of Nondestructive Testing. 53(7) (2017) 520—529.
9. Nikitina M., Grebenikova N., Dudkin V., Batov Y., Methodology for assessing the adverse effects of the use of nuclear energy on agricultural land, IOP Conference Series: Earth and Environmental Science. 390(1) (2019) 012024.
10. Gryznova E., Batov Y., Rud V., Methodology for assessing the environmental characteristics of various methods of generating electricity, E3S Web of Conferences. 140.
11. Davydov R.V., Antonov V.I., Yushkova V.V., Smirnov K.J., A new method of processing a pulse wave in rapid diagnosis of the human health, Journal of Physics: Conference Series. 1400(6) (2019) 066037.
12. Antonov V.I., Badenko V.L., Davydov R.V., Maslikov V.I., Molodtsov D.V., Modeling parameters of the flood control facilities adapted to climate change, Journal of Physics: Conference Series.1236(1) (2019) 012049.
13. Davydov R.V., Antonov V.I., Molodtsov D.V., Computer implementation of the mathematical model for water flow management by a hydro complex. Journal of Physics: Conference Series.1135(1) (2018) 012088.
14. Kuzmin M. S., Rogov S. A., On the use of a multi-raster input of one-dimensional signals in two-dimensional optical correlators, Computer Optics. 43(3) (2019) 391—396.
15. Davydov R., Antonov V., Moroz A., Parameter Control System for a Nuclear Power Plant Based on Fiber-Optic Sensors and Communication Lines, In: IEEE International Conference on Electrical Engineering and Photonics (EExPolytech), Saint Petersburg, Russia.
16. Davydov V. V., Kruzhalov S. V., Grebenikova N. M., Smirnov K. J., Method for Determining Defects on the Inner Walls of Tubing from the Velocity Distribution of the Flowing Fluid, Measurement Techniques. 61(4) (2018) 365-372.
17. Dyumin V., Smirnov K., Myazin N., Charge-coupled Device with Integrated Electron Multiplication for Low Light Level Imaging, Proceedings of the 2019 IEEE International Conference on Electrical Engineering and Photonics, EExPolytech. 8906868 (2019) 308-310.
18. Myazin N. S., Dudkin V. I., Grebenikova N. M., On the Possibility of Express Recording of Nuclear Magnetic Resonance Spectra of Liquid Media in Weak Fields, Technical Physics. 63(12) (2018) 1845-1850.
19. Grevtseva A. S., Smirnov K. J., Rud V. Yu., Development of methods for results reliability raise during the diagnosis of a person's condition by pulse oximeter, Journal of Physics: Conference Series. 1135(1) (2018) 012056.
THE AUTHOR
MAKEEV Sergey
st_makeev@mail.ru
ORCID: 0000-0003-1669-0539
Received 23.07.2022. Approved afterreviewing 07.09.2022. Accepted 14.09.2022.
© Peter the Great St. Petersburg Polytechnic University, 2022
