Mathcad пакеті көмегімен периодты электрлік сигналдарға  гармоникалық талдау жасау

B.S.  Zheldybayeva; G.R.  Koshchanova; A.G.  Amangosova; B.A.  Dzhugembayeva; G.B.  Turebayeva; A.K.  Kasymkhanova; Sh.J.  Syrbaeva; L.S.  Kainbayeva; B.А.  Mukushev

doi:10.26577/RCPh96120269

Authors

B.S. Zheldybayeva Shakarim state university, Semey, Kazakhstan https://orcid.org/0000-0003-2944-197X
G.R. Koshchanova Sh. Yesenov Caspian university of technology and engineering, Aktau, Kazakhstan https://orcid.org/0000-0001-5716-3415
A.G. Amangosova Kh. Dosmukhamedov Atyrau university, Atyrau, Kazakhstan https://orcid.org/0000-0003-2471-6081
B.A. Dzhugembayeva Kh. Dosmukhamedov Atyrau university, Atyrau, Kazakhstan https://orcid.org/0009-0002-9154-2480
G.B. Turebayeva A.Saginov Karaganda technical university, Karaganda, Kazakhstan https://orcid.org/0000-0002-8800-174X
A.K. Kasymkhanova A.Saginov Karaganda technical university, Karaganda, Kazakhstan https://orcid.org/0009-0005-4794-2585
Sh.J. Syrbaeva Kh. Dosmukhamedov Atyrau university, Atyrau, Kazakhstan https://orcid.org/0000-0003-1546-8899
L.S. Kainbayeva Korkyt Ata Kyzylorda university, Kyzylorda, Kazakhstan https://orcid.org/0000-0002-2927-6575
B.А. Mukushev S. Seifullin Kazakh agrotechnical research university, Astana, Kazakhstan https://orcid.org/0000-0001-8015-1586

DOI:

https://doi.org/10.26577/RCPh96120269

14 9

Keywords:

Fourier series, even and odd functions, Mathcad application software package, inharmonic electrical signals, computational experiment, approximation, graphical, numerical and analytical solutions

Abstract

The article considers the harmonic analysis of periodic non-sinusoidal oscillations by Fourier series expansion. The features of decomposition of even and odd functions are revealed. Based on the symbolic method, the Fourier series was presented in a complex form. Examples are presented to provide clarity of the steps of the procedures for decomposing a function into a Fourier series.

Examples of Fourier series decomposition of periodic non-sinusoidal electric currents or signals using the Mathcad application software package are considered. Graphical, numerical, and analytical solutions of non-sinusoidal periodic currents or signals have been obtained using computational experiments. Methods for calculating the sum of the terms of the Fourier series for non-sinusoidal periodic signals, which consist of several stages, are presented.

It has been proven that complex even and odd functions describing periodic currents that are not sinusoidal (or cosine-shaped) consist of the sum of simple harmonic electrical oscillations. These fluctuations make up the frequency spectrum of these currents. The results of the approximation of periodic signals are presented as a Fourier series over the interval (p, p). Electrical signals are classified into a Fourier series, and the sum of the first two and four terms of this series is obtained. It has been shown that the more members of the signals classified in a row, these members more accurately describe the signal under study.

Author Biographies

B.S. Zheldybayeva, Shakarim state university, Semey, Kazakhstan

candidate of pedagogical sciences, Shakarim State University, Semey, Kazakhstan, e-mail: balgun@mail.ru

G.R. Koshchanova, Sh. Yesenov Caspian university of technology and engineering, Aktau, Kazakhstan

candidate of pedagogical sciences, professor, Sh. Yesenov Caspian university of technology and engineering, Aktau, Kazakhstan, e-mail: koshanova.k@mail.ru

A.G. Amangosova, Kh. Dosmukhamedov Atyrau university, Atyrau, Kazakhstan

candidate of chemical sciences, assistant professor of the department of physical and technical disciplines, Kh. Dosmukhamedov Atyrau university, Atyrau, Kazakhstan, e-mail: amangosova1961@mail.ru

B.A. Dzhugembayeva, Kh. Dosmukhamedov Atyrau university, Atyrau, Kazakhstan

master physicist, senior lecturer of the department of physical and technical disciplines, Kh. Dosmukhamedov Atyrau university, Atyrau, Kazakhstan, e-mail: amangosova1961@mail.ru

G.B. Turebayeva, A.Saginov Karaganda technical university, Karaganda, Kazakhstan

master physicist, senior teacher of the physics department, A.Saginov Karaganda technical university, Karaganda, Kazakhstan, e-mail: gulnara83.12.06@mail.ru

A.K. Kasymkhanova, A.Saginov Karaganda technical university, Karaganda, Kazakhstan

master of physics, assistant professor of the department of physics, A.Saginov Karaganda technical university, Karaganda, e-mail: aknur_kassymkhanova@mail.ru

Sh.J. Syrbaeva, Kh. Dosmukhamedov Atyrau university, Atyrau, Kazakhstan

candidate of pedagogical sciences, assistant professor, Kh. Dosmukhamedov Atyrau university, Atyrau, Kazakhstan, e-mail: syrbaeva@bk.ru

L.S. Kainbayeva, Korkyt Ata Kyzylorda university, Kyzylorda, Kazakhstan

candidate of pedagogical sciences, A.Saginov Karaganda technical university, Kyzyl-Orda, Kazakhstan, e-mail: larissa_kain@mail.ru

B.А. Mukushev, S. Seifullin Kazakh agrotechnical research university, Astana, Kazakhstan

professor, doctor of pedagogical sciences, S. Seifullin Kazakh agrotechnical research university, Astana, Kazakhstan, e-mail: mba-55@mail.ru

References

Әдебиеттер

Nic Roberts, Neil Phillips, Roshan Weerasekera, Andrew Adamatzky. Propagation of electrical signals by fungi // Biosystems. Volume 229, July 2023, 104933. https://www.sciencedirect.com/science/article/pii/S0303264723001089

Uwaydah Leith. Мodeling a Periodic Signal Using Fourier Series // Journal of Applied Mathematics and Physics > Vol.12 No.3, March 2024 DOI: 10.4236/jamp.2024.123052

Satyanrayana Madgula, Venkataramana Veeramsetty, Rajababu Durgam. Signal processing approaches for power quality disturbance classification: A comprehensive review // Results in Engineering Volume 25, March 2025, 104569 https://www.sciencedirect.com/science/article/pii/S2590123025006474

Воробьев Н.Н. Теория рядов. 4 издание, перераб. и доп. - М.: Наука, 1979. - 408 с.

Жук В.В., Натансон Г.И. Тригонометрические ряды Фурье и элементы теории аппроксимации. Л.: Изд-во Ленингр. ун-та, 1983.- 188 с.

Иванов М. Т., Сергиенко А. Б., Ушаков В. Н. Теоретические основы радиотехники: Учеб. пособие. - М.: Высш. шк., 2002. - 306 с.

Баскаков С.И. Радиотехнические цепи и сигналы. - М.: Высшая школа, 1998.- 463 с.

Очков В. MathCAD 14 для студентов, инженеров и конструкторов. – Санкт-Петербург. – 2007.- 370 с.

Кирьянов Д. Mathcad 14 в подлинке. Санкт-Петербург. – 2007.- 682 с.

Мукушев Б.А. Изучение физических процессов посредством пакета MathCAD // Учебная физика – 2022. - №2. – с.45-50.

Мукушев Б.А. Пакет прикладных программ Mathcad // Вестник КазАТУ. – 2022. - №2 (113). Ч.2. – С. 197-202.

Nelson F. Using mathcad to simplify uncertainty computations in a laboratory course // Computer Applications in Engineering Education. - 2014.- Vol. 23. - № 2. - P. 250-257.

References

Nic Roberts, Neil Phillips, Roshan Weerasekera, Andrew Adamatzky. Propagation of electrical signals by fungi // Biosystems. Volume 229, July 2023, 104933. https://www.sciencedirect.com/science/article/pii/S0303264723001089

Uwaydah Leith. Мodeling a Periodic Signal Using Fourier Series // Journal of Applied Mathematics and Physics > Vol.12 No.3, March 2024 DOI: 10.4236/jamp.2024.123052

Satyanrayana Madgula, Venkataramana Veeramsetty, Rajababu Durgam. Signal processing approaches for power quality disturbance classification: A comprehensive review // Results in Engineering Volume 25, March 2025, 104569 https://www.sciencedirect.com/science/article/pii/S2590123025006474

Vorobyov N.N. Theory of series. 4th edition, revised. and add. - M.: Nauka, 1979. - 408 p.

Zhuk V.V., Natanson G.I. Trigonometric Fourier series and elements of approximation theory. L.: Publishing House of the Leningrad University, 1983. 188 p.

Ivanov M. T., Sergienko A. B., Ushakov V. N. Theoretical foundations of radio engineering: Textbook. Moscow: Higher School, 2002. 306 p.

Baskakov S.I. Radio engineering circuits and signals. Moscow: Higher School, 1998. 463 p.

Points in MathCAD 14 for students, engineers and designers. – Saint Petersburg. – 2007. - 370 p.

Kiryanov D. Mathcad 14 in the original. Saint Petersburg, 2007, 682 p.

Mukushev B.A. Studying physical processes using the MathCAD package // Educational Physics – 2022. - No. 2. – pp.45-50.

Mukushev B.A. Mathcad application software package // Bulletin of KazATU. – 2022. - №2 (113). Part 2. – pp. 197-202.

Nelson F. Using mathcad to simplify uncertainty computations in a laboratory course // Computer Applications in Engineering Education. - 2014.- Vol. 23. - № 2. - P. 250-257.