6 ECTS credits
150 h study time

Offer 1 with catalog number 4020546FNR for all students in the 1st semester at a (F) Master - specialised level.

Semester
1st semester
Enrollment based on exam contract
Impossible
Grading method
Grading (scale from 0 to 20)
Can retake in second session
Yes
Enrollment Requirements
Students must have followed 'Complex Analysis', 'Mathematical Statistics' en 'Introduction to Functional Analysis', before they can enroll for 'Harmonic and Wavelet Analysis'.
Taught in
Dutch
Faculty
Faculty of Sciences and Bioengineering Sciences
Department
Mathematics
Educational team
Ann Dooms (course titular)
Andreas Debrouwere
Activities and contact hours
30 contact hours Lecture
30 contact hours Seminar, Exercises or Practicals
Course Content

Table of contents

1  Function spaces & Fourier series

2  The Fourier transform

3. The windowed Fourier transform

4  Sampling theory

5  Frames in Hilbert spaces

6  Gabor frames

7  Continuous wavelet transformation

8  Discrete wavelet transformation

9  Multi-resolution Analysis

10 Directional transformations

Course material
Digital course material (Required) : Slides in PDF formaat
Additional info

Study material

Slides in PDF format

Course is based on:

- Boaz Porat, Digital Processing of Random Signals – Theory and Methods, Dover Publications, NY USA, 1994.

- Christian Blatter, Wavelets: A Primer, A K Peters/CRC Press, 2002.

Learning Outcomes

General competences

The student gets a modern approach of signal analysis combining functional analysis and mathematical statistics. The course entails on the one hand techniques to analyse a sampled signal form a statistical point of view and delivers the computational techniques to compute the solution and introduces on the other hand the theory of frames and wavelets to analyse signals in the time-frequency domain.

Grading

The final grade is composed based on the following categories:
Other Exam determines 100% of the final mark.

Within the Other Exam category, the following assignments need to be completed:

  • Examen andere with a relative weight of 1 which comprises 100% of the final mark.

Additional info regarding evaluation

The exam consists of tasks and a written theory and exercise part.

Evaluation:
- assignments submitted during semester: 30%
- theory part exam: 50%
- exercise part exam: 20%

A student can only pass this course on the condition that he participates in all parts of the exam. The points on the tasks are retained if one participates in the second examination period.

Allowed unsatisfactory mark
The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context

This offer is part of the following study plans:
Master of Mathematics: Financial and Applied Mathematics (only offered in Dutch)
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)
Master of Teaching in Science and Technology: wiskunde (120 ECTS, Etterbeek) (only offered in Dutch)