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
- Registration for "Harmonic and Wavelet Analysis" is allowed if one is registered or has successfully accomplished 'Complex Analysis and Riemann Surfaces', 'Mathematical Statistics' en 'Introduction to Functional Analysis'.
- Taught in
- Dutch
- Faculty
- Faculty of Sciences and Bioengineering Sciences
- Department
- Mathematics
- Educational team
- Ann Dooms
(course titular)
Kurt Barbé
- Activities and contact hours
-
30 contact hours Lecture
30 contact hours Seminar, Exercises or Practicals
- Course Content
Table of Contents
- Hilbert space of stationary signals
- Random signals and conditioning
- Wold decomposition theorem
- Spectral density and factorisation
- Laplace transform and its properties
- Laplace transform and -domain
- Laplace transform of linear dynamic systems
- Wold decomposition of stationary signals using the Laplace transform
- Non parametric spectral analysis
- Periodogram
- Time windows and leakage
- Weighted and windowed periodograms
- Hilbert space of non-stationary signals
- Problem statement: time-frequency analysis
- Heisenberg Uncertainty Principle
- Windowed Fourier transform
- Signal Reconstruction
- Recapitulation Fourier Analys
- Bandlimited signals and Whittaker-Shannon Sampling-Interpolation Theorem
- Bases and frames
- Wavelets
- Continuous Wavelet transform
- Discrete Wavelet transform
- Multiresolution Analysis
- Othonormal Wavelets with compact support
- Biorthogonal filters and wavelets
- 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 covers theory and exercises. The student defends his/her answers orally after a written preparation. The harmonic and wavelets part each account for 50% of the marks:
50%: Theory
20%: Exercises
30%: Group assignment (two tasks for each part per group. The marks on the project are kept for the second exam session).
The student needs to take part in all these evaluations to be able to pass the exam.
- 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)