Entry requirements

120 credits and 60 credits in mathematics with Complex analysis and Transform methods. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

On completion of the course, the student should be able to:

• 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 examination at the end of the course combined with assignments given during the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.