- test functions and distributions,
- operations on distributions (translation, dilation, differentiation, folding),
- Schwartz functions and tempered distributions,
- Fourier transformations of tempered distributions,
- wavelets and wavelet frames.
Module MAT-65-14-M-7
Distributions and Wavelets (M, 4.5 LP, AUSL)
Module Identification
Module Number | Module Name | CP (Effort) |
---|---|---|
MAT-65-14-M-7 | Distributions and Wavelets | 4.5 CP (135 h) |
Basedata
CP, Effort | 4.5 CP = 135 h |
---|---|
Position of the semester | 1 Sem. irreg. |
Level | [7] Master (Advanced) |
Language | [EN] English |
Module Manager | |
Lecturers |
+ further Lecturers of the department Mathematics
|
Area of study | [MAT-SPAS] Analysis and Stochastics |
Reference course of study | [MAT-88.105-SG] M.Sc. Mathematics |
Livecycle-State | [AUSL] Phase-out period |
Courses
Type/SWS | Course Number | Title | Choice in Module-Part | Presence-Time / Self-Study | SL | SL is required for exa. | PL | CP | Sem. | |
---|---|---|---|---|---|---|---|---|---|---|
2V | MAT-65-14-K-7 | Distributions and Wavelets
| P | 28 h | 107 h | - | - | PL1 | 4.5 | irreg. |
- About [MAT-65-14-K-7]: Title: "Distributions and Wavelets"; Presence-Time: 28 h; Self-Study: 107 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: irregular (by arrangement)
- Examination number: 86198 ("Distributions and Wavelets")
Evaluation of grades
The grade of the module examination is also the module grade.
Contents
Competencies / intended learning achievements
Upon successful completion of this module, the students have studied and understand the basic concepts of distribution theory. They have deepened their knowledge of wavelets and learnt about applications through examples. They are able to name the essential propositions of the lecture as well as to classify and to explain the connections.
They understand the proofs presented in the lecture and are able to comprehend and explain them. In particular, they are able to outline the conditions and assumptions that are necessary for the validity of the statements.
Literature
- W. Walter: Einführung in die Theorie der Distributionen,
- I. M. Gelfang, G. E. Schilow: Verallgemeinerte Funktionen I,
- W. Rudin: Functional Analysis,
- R. Strichartz: A Guide to Distribution Theory and Fourier Transform,
- G. B. Folland: Fourier Analysis and its Applications,
- I. Daubechies: Ten Lectures on Wavelets,
- S. Mallat: A Wavelet Tour of Signal Processing.
Requirements for attendance (informal)
Knowledge in the field of image processing (e.g. from the module [MAT-65-11-M-7]) is helpful, but not necessarily required.
Modules:
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-14-11-M-3] Introduction to Numerical Methods (M, 9.0 LP)
Courses
- [MAT-12-23-K-3] Introduction to Functional Analysis (2V+1U, 4.5 LP)
- [MAT-12-28-K-3] Measure and Integration Theory (2V+1U, 4.5 LP)
Requirements for attendance (formal)
None
References to Module / Module Number [MAT-65-14-M-7]
Module-Pool | Name | |
---|---|---|
[MAT-65-MPOOL-7] | Specialisation Image Processing and Data Analysis (M.Sc.) | |
[MAT-AM-MPOOL-7] | Applied Mathematics (Advanced Modules M.Sc.) | |
[MAT-RM-MPOOL-7] | Pure Mathematics (Advanced Modules M.Sc.) |
Notice