PhD Course

Gabor Analysis and Its Applications

Lectures by Ole Christensen (Technical University of Denmark) and Thomas Strohmer (University of California, Davis). Projects by Lasse Borup and Morten Nielsen (Aalborg University)

The course gives an introduction to Gabor analysis and some selected applications. The course is designed for the participants in the WAVES-program, and the idea is to provide all participants with a common platform of knowledge, and thereby facilitate the communication and interaction between the group at DTU and the group at Aalborg
University. However, other participants are welcome as well. The course will present parts of the theory for Gabor analysis (time-frequency analysis) as well as selected applications.

The talks/exercises will be given by Prof. Thomas Strohmer and Ole Christensen. The course will be evaluated based on projects, which will be prepared by Morten Nielsen and Lasse Borup.

The course consists of two parts

Part I: Theory, Applications, and Exercises
Dates: May 19-20, 2003
Place: Fr. Bajers Vej 7 - Room A4-108

Each day will start with a tutorial about theoretical properties of bases, frames, and Gabor systems. This tutorial will be given by Ole Christensen and last about 90 minutes. We will concentrate on results which are needed for the understanding of the applications. After that, the following lecture by Thomas Strohmer will concentrate on applications.  Applications to acoustic and image processing will be reviewed, and applications to wireless communication and coding will be treated in detail. Special emphasis will be given on the relationship between Gabor systems and OFDM (Orthogonal Frequency Division Multiplexing). In the evening there will be computer exercises.

Part II: Applications to concrete problems
Dates: June 16-17, 2003
Place:
Important! If you want to participate in Part II, please contact the organizers. The number of participants we can accommodate here is limited by our resources.

The main goal will be to implement the Gabor transform in Matlab, and using the Gabor transform code, to do signal processing on sound signals. Some basic applications will be to create Gabor based spectrograms of sound signals and to investigate the effect of thresholding the Gabor analysis coefficients.

Prerequisites: The participants are assumed to have some basic knowledge of Fourier analysis. Furthermore some background in the theory of orthonormal bases and frames in Hilbert spaces is needed. Referring to the book: Ole Christensen: "An introduction to frames and Riesz bases", Birkhauser 2003, the material needed can be found in sections 1.1-4, 3.2, 3.4, 3.6, 5.1, 5.4, 5.6, 5.7. If you have questions concerning the prerequisites, please contact one of the organizers.

Organizers: Ole Christensen, Arne Jensen, Morten Nielsen