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Wavelets (Wintersemester 2008/09)

Vorlesung: Mittwoch 8:00-9:30 Seminarraum 33
Freitag 8:00-9:30 Seminarraum 31
Übung: Freitag 11:30-13:00 HS 102
Dozent Prof. Dr. Andreas Rieder
Sprechstunde: Bis auf weiteres nur nach Vereinbarung,
Zimmer 3.040 Kollegiengebäude Mathematik (20.30)
Email: andreas.rieder(at)kit.edu
Zimmer IWRMM (20.52)


Wavelet analysis is a rather new, but meanwhile well established, technique for signal and image processing with various applications in other fields. For instance, the famous
JPEG2000 standard for image compression is based upon wavelets.


In this course we will learn the mathematical foundations of wavelet analysis which belong to the field of harmonic analysis. We will motivate wavelet analysis from the shortcomings of Fourier analysis with respect to time frequency representations of signals. Then we will study in detail the properties of the integral wavelet transform. The request for efficient evaluation of the wavelet transform leads to the concept of wavelet bases. Here, we will present the construction of orthogonal and bi-orthogonal wavelet systems. Finally, some applications will be discussed: de-noising, image compression, etc.


  • Louis, Maass, Rieder: Wavelets - Theory and Applications, Wiley 1997
  • Daubechies: Ten Lectures on Wavelets, SIAM 1993
  • Mallat: A Wavelet Tour of Signal Processing, Academic Press 1998
  • Stark: Wavelets and Signal Processing, Springer 2005