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.


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:


This page is maintained by Arne Jensen.
Updated November 18, 2003, Arne Jensen.