Welcome to the course: TMA462 (Chalmers)/MMA410 (GU)
• Our focus will be on the wavelet and (discrete) Fourier analysis based on weak formulations (in distribution sense).

• The schedule for the course can be found via the link to webTimeEdit top of the page.

• Latest news
• Latest news will appear in the course diary

• Some files are not available/constructed yet. They will appear gradually and on time for your usage.
• Teachers
Teaching assistant: Kristin Kirchner
lab Supervisor: Kristin Kirchner (e-mail address: kristin.kirchner)
Course literature

Schema
Preliminary suggestion looks as the following 4 occasions.

Day Hours
MON 8-10, Pascal
MON 10-12, MVH12
WED 13-15, Pascal
THU 13-15, MVF26

Programme: Preliminary plan for lectures and classes<

Lectures
Week Chapter
Contents
1 Distributions and the Fourier transform
2
Sampling, the FFT, the Hilbert transform, Exercise class
3
Multidimensional transforms, Exercise class
4
the Hankel transform, the Radon transform, Exercise class
5
Wavelets and filter banks, Exercise class
6
Multiresolution analysis, Exercise class
7
Wavelet bases, applications, Exercise class
8
Reserve time and repetition, Exercise class

Recommended exercises
Week Excersises
2 Exercises 1: Instructor site/ (Course site) From Bracewell: 2.10, 2.13, 2.15, 2.17, (3.10), 3.12, 3.20, 3.22
3 Exercises 2: Instructor site/ (Course site) From Bracewell: 5.29, 6.1, 6.3, 6.5, 6.9, 6.15
4 Exercises 3: Instructor site/ (Course site) From Bracewell: 6.32, 8.1, 8.3, 8.7, 8.11, 8.23, 8.29
5 Exercises 4, From Bergh etal: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.1, 3.2, 3.4, 3.6, 3.7
6 Exercises 5, From Bergh etal: 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12
7 Exercises from old Exams (2005, 2012, 2014)
8 OBS! Exta Exercises from old Exams (2005, 2012, 2014)

Computer labs

Reference literature:
Tobin A. Driscoll, Learning MATLAB, ISBN: 978-0-898716-83-2 (The book is published by SIAM)
Course requirements
A good knowledge of Fourier analysis, distribution theory and pde is helpful, however, not required.
Assignments
The assignments are titled FFT, Introduction to Wavelets, and Image Compression. The software program Matlab with tool-boxes is accessible within the student computer system. Click for downloads:
• FFT manual in lab1.pdf; Please try different signals (e.g. sums of a few sine and cosines) to try out filtering.
For the high- and low-pass filters you may use H and G of the first example on page 46 in the lecture notes (part 3).
Here is an example on how to work with Assignement 1.
• Introduction to Wavelets manual in pdf
(and to carry out the lab you will also need to download the file signals.mat);
• Image Compression manual in image1
• Image Compression manual in pdf
• Lab3 and some additional course files: image2A , image2B , compress, dctcompress, cshow,

• Notice: You need to hand in solutions for assignments 1 and 3. You do not need to hand in assignment 2.
However, to prepare for assigment 3, it is useful that you are familiar with assignment 2.

You may work in a group of two persons or individually. All hand-in shall be composed for the group or the individual person. (However, when working with the assignments, cooperation among the groups is encouraged.) The hand-ins should be delivered in the form of a pdf-file sent to the examinor no later than the date of the written exam. The reports should be sufficiently complete to be read independently.

Examination

The examination will be based on the hand-in from three computer assignments, together with a written examination.
Written examination:
There will be three opportunities to sit the written examination. Please consult the Student Portal for exact dates and location.

The written examination consists of 5 questions (4 problems and 1 theory from the list below) with a maximum credit of 5 points per question.

At least 12 points are required to pass the examination. The duration of the exam is four hours. Bring ID and receipt for your student union fee.

You should be able to state and explain all definitions and theorems given in the course and also apply them in problem solving.
During the exam no aids are allowd. However, a list of common formulas will be attached to the exam-thesis. Diversity of the course material complicates the performance of "open-book exam" for the controlers.

You will be notified the result of your exam by email from LADOK (This is done automatically as soon as the exams have been marked and the results are registered). The exams will then be kept at the students' office in the Mathematical Sciences building. Check that the number of points and your grade given on the exam and registered in LADOK coincide. Complaints of the marking should be written and handed in at the office. There is a form you can use, ask the personal in the office.)

Examination procedures
In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers.
At the link Schedule you can find when exams are given for courses at University of Gothenburg.
At the exam, you should be able to show valid identification.
Before the exam, it is important that you report that you want to take the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, so sign up via GU's Student Portal.

You can see your results in Ladok by logging on to the Student portal.

At the annual examination:
When it is practical a separate review is arranged. The date of the review will be announced here on the course website. Anyone who can not participate in the review may thereafter retrieve and review their exam on Mathematical sciences Student office, open hours. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination:
Exams are reviewed and picked up at the Mathematical sciences Student office, open hours. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.
Old exams