| Popis: |
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. |
