Time-frequency analysis and applications in information theory (Zeit-Frequenz Analyse und Anwendungen in der Informationstheorie)Contents:
This course discusses time-frequency analysis tools such as wavelets and Gabor systems which have had great impact on signal processing and communications engineering over the past 25 years. We cover the finite dimensional setting, including some results of applications of compressive sensing in time-frequency analysis. The course is suitable for mathematically inclined electrical engineers and mathematicians on the graduate student level, i.e., being in the final two years of their MSc studies. Educational objectives:
Participating students will receive a solid background on many aspects of modern time-frequency analysis. Students will recognize the usefulness of discussed tools and function spaces to analyze functions as well as operators that are well described in, respectively on phase space. Moreover, students will understand the cross fertilization between time-frequency analysis and various disciplines of electrical engineering such as communications engineering and information theory. Educational methods: lectures, exercises
Media: blackboard Level: Master
Duration: 1 Semester (WS 13/14), lectures will be held in January and February on 12 dates with weekly exercises
Exam: oral (20 min.) Prerequisites (recommended): Bachelor, Measure- and Integration theory, basics in Functional Analysis and Fourier Analysis Literature:
- Karlheinz Gröchenig: Foundations of Time-Frequency Analysis. Birkhäuser, 2001.
- Eds. P. G. Casazza and G. Kutyniok, Finite Frames: Theory and Applications, Birkhäuser, Boston (2012)