Uloga Fourierovih redova u inženjerstvu okoliša

undergraduate thesis

• Title (english): The role of Fourier series in environmental engineering
• Author: Maja Vrček
• Mentor: Sanja Kovač (mentor)
• Mentor: Davor Stanko (komentor)
• Committee member: Igor Petrović (predsjednik povjerenstva)
• Committee member: Sanja Kovač (član povjerenstva)
• Committee member: Davor Stanko (član povjerenstva)
• Committee member: Mario Gazdek (član povjerenstva)
• Granter: University of Zagreb; Faculty of Geotechnical Engineering; Varaždin
• Defense date and country: 2020-09-18, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Interdisciplinary Technical Sciences; Environmental Engineering

Abstract

Fourierov red rastavlja periodične funkcije u sume funkcija sinusa i kosinusa. Definirat ćemo njihovo dobivanje, te ćemo ih naposljetku transformirati pomoću dobivenih zapisa koeficijenata. Također ćemo navesti i vrste funkcija, odnosno periodične i neperiodične funkcije, te razlike između njih. Navest ćemo i parne i neparne funkcije.
Nakon teorije slijedi primjena Fourierovih redova u inženjerstvu okoliša pri čemu ćemo navesti nekoliko vrsta mjernih sustava, te podatke koji oni prikupljaju. Mjerni sustavi nam služe za prikupljanje različitih podataka o raznim fizikalnim veličinama nekih prirodnih pojava. Navest ćemo njihovu podjelu, opisati svaku vrstu mjernog sustava, te navesti i neke primjere. Ti podaci, odnosno brojčane vrijednosti fizikalnih ili kemijskih veličina koje su zapisane u digitalnom obliku, a koje se mogu zapisati u obliku periodičnih funkcija, a potom i pomoću suma te harmonijskih redova sinusa i kosinusa iz kojih se naposljetku dobivaju Fourierovi redovi. Najvažnija podjela signala je ona na digitalne i analogne. Analogni signal je vremenski kontinuirani signal čija se amplituda odnosno jačina mijenja neprekidno i kontinuirano s vremenom, dok digitalni signal sadrži diskretne funkcije, koje se dobivaju uzorkovanjem zapisa stanja analognog vala u određenim vremenskim koracima čija dužina zavisi o učestalosti, odnosno o frekvenciji signala. Drugim riječima, za dobivanje digitalnog signala iz analognog signala, potrebno je koristiti FFT, odnosno brzu Fourierovu transformaciju. Navest ćemo i druge vrste signala, koje ćemo potom objasniti te navesti primjere za navedene signale. Iz niza funkcija vremena dobivamo spektre.

Abstract (english)

Fourier series dissembles periodical functions into the sum of functions from sinuses and cosinuses. We will define the theory of Fourier series, which we will transform with the help of Fourier coefficients. We will list types of functions, like periodical, aperiodical function, and odd and steam functions, and their differences.
We will list a few types of measuring sensors, and adduce the types of data they collect. With usage of measuring sensors, we collect data, or variables of various physical or chemical values of natural phenomena. We will list their classification, and say something about each, and adduce some of their examples. That data, or numeric chemical or physical variables written in digital shape, can be written in the form of periodic functions. The periodic functions can then be written in the form of sums and harmonic series of sinus and cosinus from which the Fourier series are formed. The periodic functions are called signals. We will induce some of the types of signals, among which we will define analog and digital signals. The difference between thise two types of signals is that the analog signal is a time continuous signal which amplitude changes with time constantly and continual with time, whereas the digital signal is formed by discrete functions which we get by sampling of the record of the state of analog signal in certain time pitches which length depends on the frequency of the signal. In other words, for getting the digital signal from the analog signal, we need to use Fast Fourier Transformation, or FFT. We will list other types of signals also, which will be explained and few examples will be shown. From a series of time functions, we get spectres. We will explain what spectres are and list few of their examples.

• Keywords: Fourierov koeficijent; Fourierov red; signali; mjerni senzori; spektri
• Keywords (english): Fourier coefficients; Fourier series; sensors; signals; spectrum
• Language: croatian
• URN:NBN: urn:nbn:hr:130:280976
• Study programme: Title: Environmental Engineering; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/ baccalaurea) inženjer/ inženjerka inženjerstva okoliša (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/ baccalaurea) inženjer/ inženjerka inženjerstva okoliša)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-10-20 07:48:48