Fourier and Wavelet Analysis, 2nd quarter, 06/07

The course will, on request, be given in English.

Welcome to this course!

The course treats the Fourier transform and some related transforms with applications to signal and image processing. In particular, we treat issues concerning discretization (sampling, for example) and a latter time tool, 'wavelets', which enables a new practical approach to the fundamental problem that signals with sharply defined frequencies are widely extended in time (and conversely).

The course starts with an introduction to generalized functions (tempered distributions); if anything more than the Dirac delta is required - as, for example, in the sampling of signals - it is useful to have some knowledge of the theoretical base for the calculations.

Literature

Bergh, Notes on Generalized Functions and Fourier Transforms, compendium, Chalmers and Göteborg University. Click to download in pdf.
Bergh-Ekstedt-Lindberg, Wavelets, Studentlitteratur, 1999. Click to download amendments in pdf.
Bracewell, The Fourier Transform and Its Applications, McGraw-Hill, 2000.

Examination

The examination will be based on the hand-in from three computer assignments, together with a minor written examination. All hand-in shall be composed individually, and be delivered in the form of paper print-out. (However, when working with the assignments, cooperation is encouraged.)

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;
Introduction to Wavelets manual in pdf (and, if you don't work in the studat system, signals);
Image Compression manual in pdf (and, if you don't work in the studat system, files).

There will be three opportunities (in December, January, and August) to sit the written examination. The first two opportunities will be on December 21, afternoon, in the V-rooms, and on January 19, morning, in the V-rooms.
(December 22) The December 21 papers have been marked; the results will be announced when the secretaries are back next week after Christmas.

Click to down-load a course evaluation form. Please print the document, fill in your assesments, and deliver the form to the department secretariat.

Click to download some previous examination papers, with suggested solutions:
The December '05 paper in pdf; solutions in pdf.
The January '06 paper in pdf; solutions in pdf.
The August '06 paper in pdf; solutions in pdf.

Hours and rooms

Tue 8-12 in MV:F21
Thu 13-17 in MV:F21.

Professors

Jöran Bergh (examiner) and Kjell Holmåker.

Weekly plan

w 1

Distributions and Fourier transforms: Be 1, Br 1-4.

Recommended exercises are Br 2:10,13,17; 3:12,10,20,23; Be 2,3,7.

w 2

Calculation of transforms etc., sampling: Be 1, Br 6-10.

Br 5:29; 6:1,2,3,5,9,15,32; 8:1,3,6,7,11,23,29; Be 11,13.

w 3-4

Multidimensional Fourier transform, Radon, Hankel, and Hilbert transform, FFT: Be 2,4, Br 11,13,14.

Br 9:2,3; 10:5,21,30,31; 11:5,10; 13:2,3,19,20,21,23,34; 14:27.

w 5

Wavelets and filter banks: BEL 1-3.
Hand-in of FFT.

All exercises in BEL 1-3.

w 6

Multiresolution analysis: BEL 4.
Hand-in of Introduction to Wavelets.

All exercises in BEL 4.

w 7

Time in reserve and for repetition.
Hand-in of Image Compression.

Last modified: Wed Jan 3 11:40:54 CET 2007