Original title: Legendreova ortogonální báze a její využití pro získání spektra signálů
Translated title: Application of Legendre basis for spectral analysis
Authors: Mesárošová, Michaela ; Jirgl, Miroslav (referee) ; Mihálik, Ondrej (advisor)
Document type: Bachelor's theses
Year: 2021
Language: slo
Publisher: Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií
Abstract: [slo] [eng]
Práca sa zameriava na možnosti využitia Legendreovych polynómov za účelom získavania spektra signálov. Skúma ich vlastnosti v časovej a frekvenčnej doméne, akými sú napríklad spôsoby generovania, poloha koreňov a ortogonalita. Ďalším cieľom bolo implementovať Legendreovu transformáciu a overiť kvalitu získaných spektier a aproximácií signálov v porovnaní s rôznymi metódami. V závere sa zaoberá výberom vhodného aproximačného rádu ako aj analytickými možnosťami výpočtu spektra. The thesis focuses on the possibilities of using Legendre polynomials in order to obtain a spectrum of signals. It examines their properties in the time and frequency domain such as generating methods, root position, and orthogonality. Another goal was to implement the Legendre transform and to verify the quality of the obtained spectra and signal approximations in comparison with various methods. Finally, it deals with the choice of a suitable approximation order as well as the analytical possibilities of spectrum calculation.
Keywords: band-limited signal; Bessel function of the first kind; Fourier transform; Hilbert space; irregular sampling; Legendre polynomials; spectrum

Institution: Brno University of Technology (web)
Document availability information: Fulltext is available in the Brno University of Technology Digital Library.
Original record: http://hdl.handle.net/11012/198363

Permalink: http://www.nusl.cz/ntk/nusl-443777


The record appears in these collections:
Universities and colleges > Public universities > Brno University of Technology
Academic theses (ETDs) > Bachelor's theses