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Theory of Wavelets - NMNV564

Title:	Teorie waveletů
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2014 to 2017
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Václav Kučera, Ph.D.
Class:	M Mgr. NVM M Mgr. NVM > Volitelné
Classification:	Mathematics > Numerical Analysis
Incompatibility :	NNUM017
Interchangeability :	NNUM017
Is interchangeable with:	NNUM017

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Annotation -

Last update: T_KNM (28.04.2015)

The course will deal with the basis of wavelet theory in relation to numerical mathematics. Basic constructions and properties of discrete and continuous wavelets and wavelet transforms are presented.

Literature - Czech

Last update: KUCERA4 (20.09.2013)

K. Najzar, Základy teorie waveletů, skripta, Nakladatelství Karolinum, Praha, 2004

I. Daubechies, Ten lectures on wavelets, CBMS Lecture Notes 61, 1992

Syllabus -

Last update: KUCERA4 (20.09.2013)

Discrete Fourier and wavelet transform. The continuous Fourier and wavelet transform.

Multiresolution analysis and orthonormal wavelet bases. Wavelet expansion and approximation, analysis and synthesis, compression.

The Mallat algorithm. Wavelets with compact support and their computation.

The Haar and Daubechies wavelet. Coifman wavelet system. Spline wavelets. Biorthogonal wavelets and wavelets in two dimension.

Some applications of wavelets to problems in numerical analysis and data compression.

Entry requirements -

Last update: KUCERA4 (20.09.2013)

Fundamentals of numerical mathematics, mathematical analysis and functional analysis.