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Course, academic year 2016/2017

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Theory of Splines and Wavelets 2 - NNUM017

Title:	Teorie spline funkcí a waveletů 2
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2013 to 2017
Semester:	summer
E-Credits:	6
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
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Václav Kučera, Ph.D.
Classification:	Mathematics > Numerical Analysis
Interchangeability :	NMNV564
Is incompatible with:	NMNV564
Is interchangeable with:	NMNV564

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KNM (18.05.2008)

The subject of this course is the treatment of wavelets theory. It contains: continuous Fourier and wavelet transform, multiresolution, discrete wavelet transform, pyramid algorithms, basic properties of wavelets, Daubechies wavelets, Coifman wavelets, spline wavelets, compression and reconstruction. In the tutorials, some simple problems are solved on computers.

Aim of the course -

Last update: T_KNM (18.05.2008)

The aim of this course is presenting wavelet theory and some applications. Tutorials contain tests of the algorithm for compression and Mallat's algorithm of wavelet transform on computers. Students will construct graphs of some special wavelets.

Literature -

Last update: T_KNM (18.05.2008)

K. Najzar, Základy teorie waveletů (Foundamentals of wavelet theory), skripta (lecture notes), Nakladatelství Karolinum, Praha, 2004

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

Teaching methods -

Last update: T_KNM (18.05.2008)

The course consists of lectures in a lecture hall and tutorials in a computer laboratory.

Requirements to the exam -

Last update: T_KNM (18.05.2008)

Examination according to the syllabus and tests of given algorithms.

Syllabus -

Last update: T_KNM (18.05.2008)

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: KNAJ/MFF.CUNI.CZ (18.04.2008)

Fundamentals of numerical mathematics, mathematical analysis and functional analysis.

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