course-details-portlet

MA8104

Wavelets and related areas

Credits 7.5
Level Doctoral degree level
Course start Autumn 2025
Duration 1 semester
Language of instruction English
Location Trondheim
Examination arrangement Oral examination

About

About the course

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 will be taught as needed. If there are few PhD students, the course is only given as a guided self-study.

Course materials

Will be announced at the start of the course.

Subject areas

  • Analysis

Contact information

Course coordinator

Department with academic responsibility

Department of Mathematical Sciences

Examination

Examination

Examination arrangement: Oral examination
Grade: Passed / Not Passed

Ordinary examination - Autumn 2025

Oral examination
Weighting 100/100 Examination aids Code E