Faculty of Engineering and Science
The International Doctoral School of Technology and Science
The official description of the course etc. can be found here.
A brief description of the contents of the course follows below. The
topics for December are those planned at present.
- November 10
- Introduction to the course. Review of the Fourier transform and
Fourier series. Introduction to the discrete wavelet
transform. Introduction to wavelet packet transforms and best basis
algorithm. Uncertainty principles I.
- November 11
- Review of material from yesterday. Uncertainty principles II. The
time-frequency plane. Some computer demonstrations using matlab and
Uvi_Wave. The short time Fourier transform.
- December 1
- Review of November sessions. Question session. Demonstration of
time-frequency analysis. Introduction to analysis based on
overcomplete systems (frames and dictionaries of bases).
- December 2
- Tilings of the time-frequency plane. Further demonstrations using
real world signals. Remarks on the literature.
I use the book
A. Jensen, A. la Cour-Harbo: Ripples in Mathematics - The Discrete
Wavelet Transform, Springer-Verlag 2001
for a number of the results presented in the course. More
specifically, the material in Chapters 1 - 5, together with parts of
Chapters 8 and 9, were presented in the
You will also need the material in Chapters 13 and 11 for your
The following material for the
course is available:
- Slides from November 10, 2003 are here
in .pdf format.
- The home page for the Ripples book is here. On it you
will find an updated version of the Uvi_Wave toolbox, as well as all
the example files from the book.
- Examples and exercises, with m-files, are here.
This page is maintained by Arne
Updated November 18, 2003, Arne Jensen.