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.
The assignments are titled FFT, Introduction to Wavelets,
and Image Compression. Computer
accounts will be distributed in connection with the lecture on
Tuesday, November 15, and will thereafter be available at Helpdesk
only.
Click for downloads:
FFT manual
in the format
pdf or in ps;
Introduction to
Wavelets manual in pdf/ps and
signals;
Image
Compression manual in pdf/ps and
files.
There will be three opportunities (in December, January, and August)
to sit the written examination. The first two opportunities have been
on December 15, and on January 9. The third opportunity will be on August 26.
Click to down-load some previous
examination papers, with suggested
solutions:
The December 04 paper in pdf/ps; solutions pdf/ps, note that, in the first
solution, '0' should be '-iexp(-ix)'.
The January 05 paper pdf/ps, note that, in the first
problem, 'dimension 1' should be 'dimension 2'; solutions pdf/ps.
The August 05 paper pdf;
solutions pdf.
Recommended exercises are Br 2:10,13,17; 3:12,10,20,23; Be 2,3,7.
Br 5:29; 6:1,2,3,5,9,15,32; 8:1,3,6,7,11,23,29; Be 11,13.
Br 9:2,3; 10:5,21,30,31; 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.
All exercises in BEL 1-3.
All exercises in BEL 4.