# MA8104 Wavelets

**Messages:**

**Please contact me if you want to take an exam in this course.**(13.01.2020)- Here is a scan of notes taken by William Tell of the material treated in the course: MA8104

# Fall 2019

Franz Luef, room 940 SB2, Franz [dot] Luef [at] ntnu [dot] no

This PhD course is given every second year, and usually 4th and 5th year (Master) students take it along with PhD students.

We will study the wavelet theory as a part of a general time-frequency approach. After a brief reminder of basic facts in Fourier analysis we will discuss uncertainty principle, short-time Fourier transform, wavelet transform, multiresolution analysis, Gabor systems, frame theory, modulation spaces and elementary aspects of pseudodifferential operators.

"The theory of wavelets lies on the boundaries between (1) mathematics (2) scientific calculation (3) signal processing (4) image processing. The aim of the theory is to give a coherent set of concepts, methods and algorithms met in each of these disciplines"

Yves Meyer (Abel prize laureate, 2017)

- The level is suitable for good students starting from the third year of study.
- It can be taken as a regular course (MA8104) or a 'fordypningsemne' (TMA4505).
- Prerequisites: TMA4170 Fourier Analysis (recommended), Matematikk 4 (obligatory)