Gibbsov fenomen : delo diplomskega seminarja

Kerševan, Sandra (author), Dragičević, Oliver (mentor)

Gibbsov fenomen je pojav, ki ga lahko opazimo, ko gledamo delne vsote Fourierove vrste v bližini točke nezveznosti drugače zvezne funkcije. Ne glede na to, da je neskončna Fourierova vrsta enaka funkciji, ki jo aproksimiramo, povsod, kjer je ta zvezna, njene delne vsote vedno presežejo vrednost funkcije v skoku za fiksno vrednost, ki je odvisna samo od leve in desne limite funkcije v točki nezveznosti ter sinusovega integrala, izračunanega v vrednosti $\pi$. Ta fenomen se pojavi pri vseh zveznih funkcijah s končnim številom točk nezveznosti.

• Language: Slovenian
• Keywords: Gibbsov fenomen, Fourierove vrste, odsekoma zvezne funkcije
• Work type: Final seminar paper
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2019
• PID: 20.500.12556/RUL-110218
• UDC: 517.52
• COBISS.SI-ID: 18820697
• Publication date in RUL: 13.09.2019

Secondary language

• Language: English
• Title: Gibbs phenomenon

Abstract

Gibbs phenomenon is a occurrence which can be observed when we look at the partial sums of the Fourier series near the point of discontinuity of otherwise continuous function. Although the infinite Fourier series is equal to the function that we approximate where the function is continuous, partial sums always exceed the value of the jump function for a fixed value that depends only on the left and right limits of the function at the point of discontinuity and the sinus integral calculated in the value $\pi$. This phenomenon occurs for all continuous functions with a finite number of points of discontinuity.

• Keywords: Gibbs phenomenon, Fourier series, piecewise continuous functions