Wavelets

Module MA5046

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

MA5046 is a semester module in English language at Master’s level which is offered irregular.

This Module is included in the following catalogues within the study programs in physics.

  • Catalogue of non-physics elective courses
Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions

Content

Wavelet transforms, Riesz basis and frames, multiscale analysis and construction of wavelet basis, spline wavelets, biorthogonal wavelets, wavelet decomposition and functions spaces, applications of wavelet analysis

Learning Outcome

At the end of module the students have mathematical understanding of basic wavelets techniques and are able to analyse functions by wavelet transform and wavelet decomposition. They can apply these wavelet techniques in different fields and have programming skills for wavelet approximation.

Preconditions

MA1302 Introduction to Numerical Analysis, MA2302 Numerical Analysis, MA3001 Functional Analysis, MA2003 Measure theory and Integration

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

The module consists of the lecture supplemented by an exercise session. The lecture material is presented on the blackboard. The students are encouraged to study course references and course subjects. The exercise session consists of theoretical exercises. In the theoretical exercises students will work under instructor assistance on assignments, sometimes in teamwork. The exercises contribute to a better understanding of the lecture materials.

Media

blackboard lecture, numerical demonstrations, exercises

Literature

(1) I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992. (2) M. Pereya, L. Ward, Harmonic Analysis (From Fourier to Wavelets), AMS, 2012

Module Exam

Description of exams and course work

The examination is a 90 minutes' written test without any auxiliary resources. The students are asked to explain basic properties of wavelets and their mathematical derivation. They demonstrate their ability to analyse functions and function spaces by wavelet transforms and wavelet decomposition. They can read, understand, and write short numerical programmes for wavelet approximation schemes.

Exam Repetition

There is a possibility to take the exam at the end of the semester.

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