Fourier and Wavelet Analysis, 2nd quarter, 04/05

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, together with a minor written examination. All hand-in shall be composed individually, and delivered in the form of paper print-out. (However, when doing the assignments, cooperation is encouraged.)

The assignments are titled FFT (manual in pdf and in ps), Introduction to Wavelets (pdf / ps), and Image Compression (pdf / ps). Computer accounts will be distributed in connection with the lecture on Tuesday, November 16, and will thereafter be available at Helpdesk only.

December 2: Due to security considerations, the computer support team have closed all student accounts for this course. The accounts may be signed for anew at Helpdesk.
Input files for the last two assignments can now also be found in the directories Lab2 and Lab3.

The two nearest opportunities to have the written examination have been determined, in consultation with the participants. The first was on Saturday, December 18, morning session, in the V building.
The December 18 thesis in pdf/ps and hints for solutions pdf/ps (an obviuos misprint in no 1) are available.

The second opportunity for the written examination was on Friday, January 14, morning session, in the M building.
The January 14 thesis in pdf/ps and hints for solutions pdf/ps are available.

There will be a third opportunity in August.

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, and will afterwards be available at the Helpdesk. The software program Matlab with tool-boxes is available from these accounts.

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: Fri Jan 14 13:13:44 MET 2005