Main page

Latest news

The first lecture is Monday 27/10 8.00-8.45. The lecture is only one hour, because of the π-day.
Please note that not all links in this web page work yet.
Lectures next week: 3/11 8-10, 6/11 8-12
Exercise class: 4/11 8-10
A list of exercises have been added to the "Course litterature". Many of these will be covered in exercise classes, but not all. Please try as may as you can before the exercise class
the notes page 21-31 have been replaced by a larger set of notes, pages 21-35, with a few extra pages in between
I have added some more exercises in the problems sheet.
NOTE! I have decided to change the order of the material in the course. Hence I will now start with filters and wavelets, and then to Fourier transforms in several variables, Hilbert and Radon transforms, et.c. later. The reason is that I whish that you start with the computer lab before the very end of the course.

Teachers

Examiner and lecturer: Bernt Wennberg (e-mail address: wennberg )
Exercises and computer project: Fredrik Lindgren (e-mail address: fredlind)

Course literature

Bergh, Notes on Generalized Functions and Fourier Transforms, compendium, Chalmers and Göteborg University. Click to download in pdf .
Bergh, Ekstedt, Lindberg: Wavelets , Studentlitteratur. It is sold at Cremona. Click to download amendments in pdf . The chapters 1-4, 5 (parts), 7 (parts) and 8 (parts) are included in the course
Bracewell The Fourier Transform and its Applications . It is sold at Cremona. Parts of chapters 1-14 are included in the course. However, lecture notes will be made available, and hence this book is not essential for the course.
Lecture notes part 1 ; part 2 ; part 3 ; part 4 ; part 5 ; part 6 ; part 7 ; part 8 ; part 9 ; part 10 ;
A list of exercises and problems here . Please look here frequently, as this page will be updated during the course.

Preliminary plan for lectures and classes

Week	Contents	Comments and suggested problems
1	Distributions and the Fourier transform
2	Sampling, the FFT, the Hilbert transform,
3	Multidimensional transforms, the Hankel transform, the Radon transform	Exercise class Thursday
4	Wavelets and filter banks	Exercise class Friday
5	Multiresolution analysis	Exercise class Wednesday
6	Wavelet bases, applications	Exercise class Friday
7	Reserve time and repetition	Exercise class Thursday

Computer labs and Matlab excercises

The assignments are titled FFT, Introduction to Wavelets, and Image Compression. The software program Matlab with tool-boxes is accessible within the studat computer system. Click for downloads:

FFT manual in pdf; Please try different signals (e.g. sums of a few sine and cosines) to try out filtering. 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 pdf
and the necessary files are available in the directory Lab3filer).

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 five problems, with a maximum credit of 5 points per problem. At least 12 points are required to pass the examination. The duration of the exam is five 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 the following aids are permitted: course litterature, lecture notes and calculator.

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 an 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 person in the office.).

The following link will tell you all about the examination room rules at Chalmers: Examination room instructions

Computer labs

All hand-in shall be composed individually. (However, when working with the assignments, cooperation is encouraged.) The hand-ins should be delivered in the form 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.
The assignments are titled FFT, Introduction to Wavelets, and Image Compression.

Course evaluation

In the beginning of the course, two student representatives for the course will be will be selected, who will meet with the lecturer in week 46 for a halftime evaluation of course. A final evaluation will then take place in the end of the course. Click to down-load a course evaluation form. Please print the document, fill in your assesments, and deliver the form to the department secretariat.

Old exam papers

Click to download some previous examination papers, with suggested solutions (please note: these should be regarded as exercises only, and not as prototypes for the examination papers to come):
The December '06 paper in pdf; solutions in pdf.
The January '07 paper in pdf; solutions in pdf.
The August '07 paper in pdf; solutions in pdf.
The December '07 paper in pdf; solutions in pdf.