6 EC
Semester 1, period 1, 2
5334WAVE6Y
Theoretical aspects: The course contains an abstract mathematical introduction on the topic of wavelets and their general construction using the concept of multiresolution analysis. Based on two concrete examples, being the classical Haar wavelet and the less know and somewhat less trivial wavelets, the more abstract concept of multiresolution analysis is introduced, and together with it the scaling function. It is shown how wavelets can be constructed from the multiresolution analysis, and hence from the scaling function. Apart from revisiting the Haar- and other wavelets. Special attention is paid to their decay, their vanishing moments and their smoothness.
Practical aspects: Apart form the theoretical aspects, we will pay attention to applications of wavelets in both linear and nonlinear approximation theory and signal processing. In particular we discuss the wavelet transform, the discrete wavelet transform and the fast discrete wavelet transform, and their implementation.
Context: The vast topic of Wavelets and Multiresolution Analysis is situated both in abstract and in applied analysis. Their existence and mathematical properties are worth studying on their own account, nonetheless they find applications in many fields, particularly in signal processing (wavelets were used in the recent detection of gravitational waves). Wavelets are well-suited to analyze irregular and non-smooth signals (such as from geophysics, finance, etc). Wavelets are also used in ingenious approximation methods for solutions of PDEs.
A Mathematical Introduction to Wavelets, by P. Wojtaszczyk. London Mathematical Society. Student Texts 37.
Introduction to the Theory of Distributions, by F.G. Friedlander and M. Joshi.
A First Course in Wavelets and Fourier Analysis, by A. Boggess and F. Narcowich.
An Introduction to Pseudo-Differential Operators, by M. W. Wong
Matlab, Python
Hand-outs by the lecturer, slides.
The course is a lecture course. However, in weeks 4 and 12, students are asked to work in pairs on assignments that they should hand in in the form of a video-presentation.
Activity | Hours | |
Tentamen | 3 | |
Self study | 165 | |
Total | 168 | (6 EC x 28 uur) |
This programme does not have requirements concerning attendance (TER-B).
| Item and weight | Details |
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Final grade | |
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1 (100%) Tentamen |
The final individual exam counts for 70%, whereas each of the assessments counts for 15%. The score for the individual exam should be at least 5 out of 10. In the event of a resit, the results for the assessments will still be valid, with the same weights. In particular, you can only resit the exam. There is no possibility to replace an assessment. The minimum score for each assessment and for the exam is 1 out of 10.
Inspection of assessed work is possible on appointment with the lecturer.
The assignments can be made in pairs, and this is even encouraged in order to facilitate students to have contact with one another in times of Corona (although individual work is allowed as well). Both students in the pair get the same grade for the assignment.
The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl
This is a new course, and it is not precisely known, and depends also on the students, which topics will be covered in which weeks. Canvas will give more details. The plan is to cover the first four Chapters of the book ``A mathematical introduction to Wavelets'' by P. Wojtaszczyk (London Mathematical Society, Student Texts 37).
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The schedule for this course is published on DataNose.