281032 Wavelets in physics and signal processing (V) (SoSe 2003)

The theory of wavelets is a relatively new and fast developing subject. Wavelets are mathematical functions that divide data into different frequency components and then study each component with a resolution matched to its scale. For example they can be advantageous compared to traditional Fourier methods in analyzing physical situations in which the signal contains sharp spikes. They were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Because of their interdisciplinary origin, wavelets appeal to scientists and engineers of many different backgrounds. Several aspects of wavelets will be discussed which include an overview on the families of wavelets, scale-varying basic functions, families of wavelets, the continuous wavelet transform, the discrete wavelet transform, the fast wavelet transform, adapted waveforms, time frequency location, construction of orthonormal wavelet bases and multiresolution analysis, Haar and Shannon wavelets, Wigner distribution for signal analysis and regularity of wavelets. Recent advances have shown wavelets to be an effective and often necessary mathematical tool for signal processing in physics and engineering sciences. Interchanges between these fields and further mathematical developments during the last ten years have led to many new wavelet applications as for example image compression or new descriptions in fluid mechanics including turbulence. In addition they have become essential in the world of information storage and retrieval and are used in computational imaging. In the accompanying seminars and exercises the students will be taught on selected applications covering a variety of scientific, using in parts the Matlab wavelet package.

Requirements for participation, required level

This course will provide an introduction to the theory of wavelet and will demonstrate how modern mathematics is integrated within computational engineering and physical applications. The lecture is designed to be accessible by higher level undergraduate students and graduate students who are familiar with the basic concepts of Linear Algebra and Analysis. The course is devoted to interested students of computer science with special emphasis on Naturwissenschaftliche Informatik?, physics and applied mathematics. The students are invited to contribute with seminars on selected topics.

Bibliography

For a comprehensive list of literature look at the webpage of the lecture:
http://www.physik.uni-bielefeld.de/~adegenha/activities.dir/wavelets.dir/wavelets.html