EXPLORING THE GIBBS EFFECT IN APPROXIMATION OF DISCONTINUOUS FUNCTIONS AND PROCESSING CONTRAST IMAGES
Authors:
Type:
Article
Pages:
from 353
to 357
Status:
Published
Received:
29.08.2014
Accepted:
10.10.2014
Published:
10.10.2014
Language:
Russian
Keywords:
the Gibbs effect, the approximation, Fourier series, image processing, numerical experiment
Abstract (English):
The work is devoted to one of the well-known problems in the approximation of functions by means of Fourier series. It is viewed the approximation of functions of one or two real variables. The latter has a relationship to the processing of two-dimensional images. The aim of work is to explore the Gibbs effect by means of a numerical experiment, which is available for students of technical university, after learning course of functional analysis. It is used mathematical package Maple.
The work is devoted to one of the well-known problems in the approximation of functions by means of Fourier series. It is viewed the approximation of functions of one or two real variables. The latter has a relationship to the processing of two-dimensional images. The aim of work is to explore the Gibbs effect by means of a numerical experiment, which is available for students of technical university, after learning course of functional analysis. It is used mathematical package Maple.
Keywords:
the Gibbs effect, the approximation, Fourier series, image processing, numerical experiment
the Gibbs effect, the approximation, Fourier series, image processing, numerical experiment
1. Kantorovich, L. V. Funktsional´nyy analiz: uchebnik, 3-e izd. / L. V. Kantorovich, G. P. Akilov, - M.: Nauka. Glavnaya redaktsiya fiziko-matematicheskoy literatury, 1984. - 752 s.
2. Tkachenko, D. S. Primenenie ryada Fur´e dlya approksiatsii izobrazheniya: illyustratsionnyy material / D. S. Tkachenko. - M: MIFI. - Rezhim dostupa: http://tkachenko-mephi.narod.ru/pdfs/ia.pdf
3. Aleksich, G. Problemy skhodimosti ortogonal´nykh ryadov/ G. Aleksich. - M.: Izd-vo inostr. Lit-ry, 1963. - 359 s.
