O diskretni Fourierovi transformaciji

delo diplomskega seminarja

Vito Založnik (Author), Pavle Saksida (Mentor)

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.

Keywords

matematika;diskretna Fourierova transformacija;hitra Fourierova transformacija;konvolucija;korelacija;načelo nedoločnosti;spektrogram;

Data

Language:	Slovenian
Year of publishing:	2021
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[V. Založnik]
UDC:	519.65
COBISS:	79812611
Views:	1351
Downloads:	165
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	About discrete Fourier transform
Secondary abstract:	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.
Secondary keywords:	mathematics;discrete Fourier transform;fast Fourier transform;convolution;correlation;uncertainty principle;spectrogram;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	28 str.
ID:	13668079