Wavelets
5 credits
Syllabus, Master's level, 1MA082
This course has been discontinued.
A revised version of the syllabus is available.
- Code
- 1MA082
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 13 March 2008
- Responsible department
- Department of Mathematics
Entry requirements
120 credit points and 60 credit points Mathematics with Complex analysis and Transform methods.
Learning outcomes
In order to pass the course the student should
- be able to use the discrete Fourier transform;
- be able to describe the relation between the discrete and the continuous Fourier transform;
- be able to compute Fourier transforms using the fast Fourier transform;
- be able to construct various wavelet bases and know how to use them as a tool for analysing functions;
- be able to describe properties of various wavelet bases;
- be familiar with multiresolution analysis;
- be able to describe computational aspects of Fourier and wavelet transforms;
- know a little about applications.
Content
The discrete Fourier transform. The fast Fourier transform. Wavelet bases for discrete and continuous variables. The Haar basis. Differentiable wavelet bases. Compact wavelet bases. Multiresolution analysis. A little about applications.
Instruction
Lectures and computer laboratory work.
Assessment
Written and, possibly, oral examination at the end of the course. Moreover, to pass the course the laboratory work should be carried out satisfactorily.