Multirezolucijski valići i diskretne transformacije

Vidović, Toni (2016) Multirezolucijski valići i diskretne transformacije. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

In this thesis we have introduced basic theory of orthonormal wavelets in one dimension. We have shown how to construct wavelets from multiresolutional analysis; however, it is important to emphasise that there are wavelets that do not arise from a multiresolutional analysis on $L^2(\mathbb{R})$. After construction, it was important to introduce simpler characterizations of orthonormal wavelets, multiresolutional analysis and associated scaling function. In the last chapter we have shown some applications of orthonormal wavelets. We introduced algorithms for data compression and data reconstruction based on wavelets, which are used, for instance, in image compression. Using wavelet packets, which are one of the tools for signal processing, we have shown how to achieve better frequency localization, if the original wavelet frequency localization was not enough.

Item Type: Thesis (Diploma thesis)
Supervisor: Bakić, Damir
Date: 2016
Number of Pages: 56
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 26 Aug 2016 08:33
Last Modified: 26 Aug 2016 08:33
URI: http://digre.pmf.unizg.hr/id/eprint/5004

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