# Faculty of Engineering and Science

The International Doctoral School of Technology and Science

#
PhD Course

## Time-Frequency Analysis

The official description of the course etc. can be found here.
### Description

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.

### Course material

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
November sessions.

You will also need the material in Chapters 13 and 11 for your
computer experiments.
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
Jensen.

Updated November 18, 2003, Arne Jensen.