20.500.12556/RUL-173615 Algebraična teorija procesiranja signalov in algoritmi za spektralno analizo delo diplomskega seminarja Algebraic signal processing theory and spectral analysis algorithms Pri obdelavi signalov ima ključno vlogo analiza frekvenčne kompozicije signalov. Frekvenčni odziv se izračuna z DFT, bolj učinkovito pa z FFT. Predstavimo klasično teorijo DSP in jo posplošimo v algebraično teorijo procesiranja signalov. Razvijemo signalni model kot trojico algebre, modula in bijektivne linearne preslikave, v modelu definiramo spekter in Fourierovo transformacijo. Predstavimo polinomski signalni model in njegove lastnosti. Pokažemo karakterizacijo skupinske zakasnitve. Izpeljemo algoritem PDFT, algoritem za grob in fin izračun odziva, ter algoritem za izračun skupinske zakasnitve. Opredelimo natančnost in računsko zahtevnost algoritma PDFT. Podamo primer uporabe algoritmov v lokalizaciji. In signal processing, the analysis of frequency composition of signals plays a key role. The frequecy response is computed with the DFT, and more effectively with the FFT. We present the classic theory of DSP and generalize it to algebraic signal processing theory. We develop the algebraic signal model as the triple, consisting of an algebra, a module and a bijective linear mapping. We define the spectrum and Fourier transform of the model. We present the polynomial signal model and its properties. We show the characterization of group delay. We derive the PDFT algorithm as well as a coarse-fine response algorithm and a group delay estimation algorithm. We determine the precision and computational complexity of the PDFT algorithm. We give an example of the use of the algorithms in localization. signalni model diskretna Fourierova transformacija polinomska algebra upodobitve algeber frekvenčni odziv skupinska zakasnitev lokalizacija signal model discrete Fourier transform polynomial algebra representations of algebras frequency response group delay localization true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2025-09-19 08:15:18 2025-09-19 08:15:23 2025-11-11 03:48:18 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 153981 250192643 19075.pdf 19075.pdf 1 FF1F3A25AF343AEEE3CC132567E9DFF1 7d07108c67bd7c528297ce465b4086a56e0a4588a0dabb17b88a88dd69f8c923 d93d82ee-951f-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=218221 Fakulteta za matematiko in fiziko 0 0 0