Fourier and Wavelet Analysis, 2nd quarter, 02/03

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 pdf / ps.
Bergh-Ekstedt-Lindberg, Wavelets, Studentlitteratur, 1999.
Bracewell, The Fourier Transform and Its Applications, McGraw-Hill, 2000.

Examination

The examination will be based on the hand-in from three computer assignments, and a minor written examination.
The assigmnents are titled FFT (manual in pdf / ps), Introduction to Wavelets (pdf / ps), and Image Compression (pdf / ps).

The written examination has been scheduled, after a consultation with the participants, to take place on December 20, 08.45-13.45 in VÖ42, and (a second opportunity) on January 17, 08.45-13.45 in MC.

Hours and rooms

Tue 8-12 in MD7,
Thu 13-17 in MD7.

Professors

Jöran Bergh (examiner) and Kjell Holmåker.

Weekly plan

w 1

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

Recommended exercises are 2:10,12,13,15,17; 3:10,12,20,22,23.

w 2

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

5:29; 6:1,2,3,5,9,15,32; 8:1,2,3,6,7,11,23,29; 9:2,3; 10:5,21,25,30,31.

w 3-4

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

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

Computer accounts will be distributed. The software program Matlab with tool-boxes is available from these.

w 5

Wavelets and filter banks: BEL 1-3. (Wavelab may also be freely down-loaded from Stanford.)
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: Mon Mar 3 08:53:57 MET 2003