Primjena diskretne Fourierove transformacije u obradi signala

master's thesis

• Title (english): Application of discrete Fourier transformation in signal processing
• Author: Mateo Fatović
• Mentor: Ivica Nakić (mentor)
• Committee member: Ivica Nakić (predsjednik povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-03-02, 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: matematički alati; obrada digitalnih slika; programski jezik Python; algoritmi za DFT; algoritmi za DCT; mijenjanje kontrasta; zaglađivanje slike; definicija tenzorskog produkta; višedimenzionalnih algoritama za FFT; višedimenzionalnih algoritama za DCT
• Keywords (english): mathematical tools; digital image processing; Python programming language; algorithms for DFT; algorithms for DCT; changing the contrast; image smoothing; definition of tensor product; multidimensional algorithms for FFT; multidimensional algorithms for DCT
• Language: croatian
• URN:NBN: urn:nbn:hr:217:698750
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-03-24 13:06:35