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master's thesis
Primjena diskretne Fourierove transformacije u obradi signala
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:698750
Fatović, Mateo
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Fatović, M. (2023). Primjena diskretne Fourierove transformacije u obradi signala (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:698750

Fatović, Mateo. "Primjena diskretne Fourierove transformacije u obradi signala." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:698750

Fatović, Mateo. "Primjena diskretne Fourierove transformacije u obradi signala." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:698750

Fatović, M. (2023). 'Primjena diskretne Fourierove transformacije u obradi signala', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:698750

Fatović M. Primjena diskretne Fourierove transformacije u obradi signala [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 November 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:698750

M. Fatović, "Primjena diskretne Fourierove transformacije u obradi signala", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:698750

Metadata
TitlePrimjena diskretne Fourierove transformacije u obradi signala
Title (english)Application of discrete Fourier transformation in signal processing
AuthorMateo Fatović
MentorIvica Nakić (mentor)
Committee memberIvica Nakić (predsjednik povjerenstva)
Committee memberSiniša Slijepčević (član povjerenstva)
Committee memberAndrej Dujella (član povjerenstva)
Committee memberMarko Vrdoljak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-03-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu pokazano je kako primjeniti matematičke alate u obradi digitalnih slika. Pri implementaciji je korišten programski jezik python. U prvom poglavlju definirani su algoritmi za DFT i DCT, kao i njihove implementacije, te je naveden i kratki opis i implementacija filtera. U drugom poglavlju objašnjeno je kako se slike reprezentiraju u računalu i kako im jednostavno mijenjati neka svojstva. Pokazana je primjena jednostavnih operacija kao npr. mijenjanje kontrasta, te primjena operacija baziranih na filterima(detekcija rubova i zaglađivanje slike). Dana je i definicija tenzorskog produkta koji je koristan kako bi se algoritmi definirani u prvom poglavlju jednostavno proširili na višedimenzionalno okruženje. Na kraju je pokazana implementacija višedimenzionalnih algoritama za FFT i DCT, te primjena tih algoritama na konkretnim primjerima.
Abstract (english)
In this thesis is shown how to apply mathematical tools in image processing. The Python programming language was used during the implementation. In the first chapter, the algorithms for DFT and DCT are defined, as well as their implementations, and a brief description and implementation of the filter is provided. In the second chapter, it is explained how images are represented in the computer and how to easily change some of their properties. The application of simple operations, such as changing the contrast, and the application of filter based operations (edge detection and image smoothing) are shown. A definition of the tensor product is also given, which is useful in order to easily extend the algorithms defined in the first chapter to a multidimensional environment. At the end, the implementation of multidimensional algorithms for FFT and DCT is shown, as well as the application of these algorithms on concrete examples.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:698750
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-03-24 13:06:35