Fourier and Wavelet Analysis, 2nd quarter, 03/04
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 assignments are titled FFT (manual in pdf /
ps),
Introduction to Wavelets (manual in pdf /
ps), and
Image Compression (manual in pdf /
ps).
The two nearest opportunities to have the
written examination have been determined, after a consultation
with the participants in the last week of November. The first
opportunity is on December 19, morning session, in the V building. The
second opportunity is on January 16, morning session, in the M
building. The third opportunity is in August.
Hours and rooms
Tue 8-12 in MD6,
Thu 13-17 in MD6.
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: Thu Dec 4 09:44:00 MET 2003