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undergraduate thesis
Fourierova serija i primjena na periodičke signale
2020. urn:nbn:hr:200:743295
Dadić, Ružica
Josip Juraj Strossmayer University of Osijek
Faculty of Electrical Engineering, Computer Science and Information Technology Osijek
Department of Core Courses
Chair of Mathematics, Physics and Mechanical Engineering

Cite this document

Dadić, R. (2020). Fourierova serija i primjena na periodičke signale (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Faculty of Electrical Engineering, Computer Science and Information Technology Osijek. Retrieved from https://urn.nsk.hr/urn:nbn:hr:200:743295

Dadić, Ružica. "Fourierova serija i primjena na periodičke signale." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Faculty of Electrical Engineering, Computer Science and Information Technology Osijek, 2020. https://urn.nsk.hr/urn:nbn:hr:200:743295

Dadić, Ružica. "Fourierova serija i primjena na periodičke signale." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Faculty of Electrical Engineering, Computer Science and Information Technology Osijek, 2020. https://urn.nsk.hr/urn:nbn:hr:200:743295

Dadić, R. (2020). 'Fourierova serija i primjena na periodičke signale', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Faculty of Electrical Engineering, Computer Science and Information Technology Osijek, accessed 21 January 2025, https://urn.nsk.hr/urn:nbn:hr:200:743295

Dadić R. Fourierova serija i primjena na periodičke signale [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Faculty of Electrical Engineering, Computer Science and Information Technology Osijek; 2020 [cited 2025 January 21] Available at: https://urn.nsk.hr/urn:nbn:hr:200:743295

R. Dadić, "Fourierova serija i primjena na periodičke signale", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Faculty of Electrical Engineering, Computer Science and Information Technology Osijek, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:200:743295

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Metadata
TitleFourierova serija i primjena na periodičke signale
Title (english)Fourier series and application to periodic signals
AuthorRužica Dadić
MentorAnita Katić (mentor)
MentorVanja Mandrić Radivojević (sumentor)
Committee memberAnita Katić (predsjednik povjerenstva)
Committee memberZdravko Krpić (član povjerenstva)
Committee memberKrešimir Grgić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Faculty of Electrical Engineering, Computer Science and Information Technology Osijek
(Department of Core Courses)
(Chair of Mathematics, Physics and Mechanical Engineering)
Osijek
Defense date and country2020-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Electrical Engineering
Telecommunications and Informatics
Abstract
U ovom radu razmatra se problematika Fourierovog reda, koji je jedna od metoda Fourierove analize. Fourierovi redovi se koriste kako bi se periodične funkcije prikazale pomoću funkcija sinus i kosinus. U prvom dijelu definirana je funkcija i njena svojstva. Budući da se Fourierovi redovi temelje na trigonometrijskim funkcijama, one su naglašene. U drugom dijelu definirani su redovi. Navedeni i objašnjeni su kriteriji konvergencije reda. Uz svaki kriterij konvergencije reda dan je primjer reda čija se konvergencija može dokazati koristeći taj kriterij. U trećem dijelu definiran je trigonometrijski Fourierov red i dani su primjeri razvoja nekih funkcija u Fourierov red. Sve formule Fourierovog reda i Fourierovih koeficijenata su izvedene. U ovom dijelu navedena je i primjena Fourierovih redova. U posljednjem poglavlju prikazani su primjeri aproksimacije signala Fourierovim redom. Predstavljen je MATLAB te su navedene i objašnjene korištene naredbe. U MATLAB-u su definirani i nacrtani trokutasti, pilasti i kvadratni signal te njihova aproksimacija Fourierovim redom.
Abstract (english)
This paper discusses the problem of the Fourier series, which is one of the methods of Fourier analysis. Fourier series are used to represent periodic functions using the sine and cosine functions. In the first part, the function and its properties are defined. Since the Fourier series is based on trigonometric functions, they are emphasized. In the second part, the series are defined. Convergence criteria are listed and explained. Each convergence criterion is accompanied by an example of a series whose convergence can be proven using that criterion. In the third part, the trigonometric Fourier series is defined and examples of the development of some functions into the Fourier series are given. All formulas of the Fourier series and Fourier coefficients are derived. The application of the Fourier series is also mentioned in this section. In the last chapter, examples of signal approximation by the Fourier series are presented. MATLAB is introduced and the used commands are listed and explained. In MATLAB, triangular, sawtooth, and square signals are defined and plotted, and their approximation by the Fourier series
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:200:743295
Study programmeTitle: Undergraduate University Study Programme in Computer Engineering
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
Type of resourceText
File originBorn digital
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Created on2020-11-13 12:49:33