20.500.12556/RUL-134756 Uporaba diskretne valčne transformacije pri analizi telemetričnih podatkov delo diplomskega seminarja Use of discrete wavelet transform in telemetry data analysis V delu je predstavljena diskretna valčna transformacija in njena uporaba pri analizi podatkov. Transformacija zaporedje podatkov z uporabo filtrov razdeli na dva dela, pri čemer se ohrani en del, drugi del pa je potreben le pri rekonstrukciji zaporedja. Ta postopek je opisan z Laurentovimi polinomi in Evklidovim algoritmom za Laurentove polinome. Vpeljan je pogoj popolne rekonstrukcije, ki zagotavlja, da je transformacija obrnljiv postopek. Predstavljen je v matrični obliki z uvedbo polifaznih komponent in polifaznih matrik filtrov. Na koncu je predstavljen še konkreten primer uporabe diskretne valčne transformacije na primeru grupiranja telemetričnih podatkov. In this thesis, the definition of discrete wavelet transform as well as its use in the data analysis field is presented. The transform works in a way that, with the use of filters, it divides a sequence of data into two parts: one part is kept for later use and the other, the second part, is used for reconstruction purposes only. This procedure is described by Laurent polynomials and Euclidean algorithm for Laurent polynomials. Furthermore the condition of perfect reconstruction, which ensures that the discrete wavelet transform is a reversible process, is introduced. The condition is represented in a matrix form, with the introduction of polyphase representation and polyphase matrix of filters. Finally, the use of discrete wavelet transform is demonstrated on an actual example of clustering of telemetry data. diskretna valčna transformacija Laurentovi polinomi Evklidov algoritem pogoj popolne rekonstrukcije polifazna predstavitev grupiranje discrete wavelet transform Laurent polynomials Euclidean algorithm perfect reconstruction condition polyphase representation clustering true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2022-01-30 08:15:01 2022-01-30 08:15:04 2024-05-29 12:30:00 0000-00-00 00:00:00 2022 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 123013 97687299 4336.pdf 4336.pdf 1 1A361A88B5323F901760145B6D565AFA 8f1a9fb2682a62f1b49b0666560d43117615f872385d540776f67ebf663ce8fb 226889d8-819c-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=153378 Fakulteta za matematiko in fiziko 0 0 0