Back to Search
Start Over
O diskretni Fourierovi transformaciji
- Publication Year :
- 2021
-
Abstract
- V delu diplomskega seminarja sem se ukvarjal s Fourierovo in diskretno Fourierovo transformacijo. Najprej sem predstavil Fourierovo transformacijo in nekaj njenih lastnosti, nato pa še motiv za diskretizacijo in vpeljavo diskretne Fourierove transformacije ter nekaj njenih lastnosti. Predstavil sem tudi postopek oziroma algoritem za hitrejši izračun diskretne Fourierove transformacije, imenovan hitra Fourierova transformacija. Glavni cilj dela diplomskega seminarja je dokaz načela nedoločnosti za Fourierovo in diskretno Fourierovo transformacijo. Formulaciji se med sabo sicer razlikujeta vendar podajata enak rezultat - nikoli ne moremo hkrati poljubno natančno vedeti kje v prostorskem in kje v frekvenčnem prostoru se nahajamo. In the diploma seminar, I studied the Fourier and discrete Fourier transforms. I first presented the Fourier transform and some of its properties, and then the motivation for the discretization and the introduction of the discrete Fourier transform and some of its properties. I also presented a algorithm for faster calculation of the discrete Fourier transform, called fast Fourier transform. The main goal of the diploma seminar is to prove the uncertainty principle for Fourier and discrete Fourier transforms. The formulations in the countinous and the discrete cases differ, but they give essentially equaivalent results. The essence of the Heisenberg principle can be stated as follows: we can never simultaneously know exactly where we are in time space and where we are in frequency space.
Details
- Language :
- Slovenian
- Database :
- OpenAIRE
- Accession number :
- edsair.od......3505..efed05117c9b08ba1dc439b88fd46367