Course - Wavelets and related areas - MA8104
MA8104 - Wavelets and related areas
About
Examination arrangement
Examination arrangement: Oral examination
Grade: Passed / Not Passed
| Evaluation | Weighting | Duration | Grade deviation | Examination aids |
|---|---|---|---|---|
| Oral examination | 100/100 | E |
Course content
The course presents an introduction to applied harmonic analysis covering the basics of time-scale analysis and time-frequency analysis. The continuous wavelet transform and the short-time Fourier transform are discussed as well as its discretization, which concerns the construction and properties of wavelet bases and Gabor frames. In this context, the relevant mathematical concepts are reproducing kernel Hilbert spaces, frames, and Riesz bases for Hilbert spaces. Applications related to areas such as signal analysis, image processing, and machine learning will be also discussed.
Learning outcome
1. Knowledge: The course presents an introduction to applied harmonic analysis covering the basics of time-scale analysis and time-frequency analysis. The continuous wavelet transform and the short-time Fourier transform are discussed as well as its discretization, which concern the construction and properties of wavelet bases and Gabor frames. In this context, the relevant mathematical concepts are reproducing kernel Hilbert spaces, frames and Riesz bases for Hilbert spaces. Applications related to areas such as signal analysis, image processing and machine learning will be also discussed.
2. Skills: The students should be able to handle problems and conduct research related to theoretical and applied problems related to wavelet theory, and, more generally, time-frequency analysis. In particular, techniques connected with signal and image processing should be studied.
3. Competence: The students should be able to participate in scientific discussions and conduct research on high international level in wavelet theory, time-frequency analysis and its applications as well as to collaborate in joint interdisciplinary research projects.
Learning methods and activities
Lectures, alternatively guided self-study.
The course is taught every second year, if there are enough students, next time Fall semester 2023. If there are few students, there will be guided self-study.
Recommended previous knowledge
Fourier analysis course, or at least Mathematics 4.
Course materials
Will be announced at the start of the course.
Version: 1
Credits:
7.5 SP
Study level: Doctoral degree level
Term no.: 1
Teaching semester: AUTUMN 2023
Language of instruction: English, Norwegian
Location: Trondheim
- Analysis
Department with academic responsibility
Department of Mathematical Sciences
Examination
Examination arrangement: Oral examination
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Autumn ORD Oral examination 100/100 E
-
Room Building Number of candidates - Spring ORD Oral examination 100/100 E
-
Room Building Number of candidates
- * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"