Mat-1.3422 Wavelet theory (3 cr L) autumn 2006
Lectures and exercise sessions
The lectures and exercise sessions, together 6 h/week during the first period are held on Tuesday, Wednesday and Thursday at 10-12 in room Y427B.
There will be around 4 hours of lectures per week and 2 hours per week exercise sessions.
Content (preliminary)
- Multiresolutions and orthonormal bases
- Construction of wavelet functions
- Computational algorithms
- Interpolation
- the continuous wavelet transform
- The ridgelet transform
Below are the approximations of a function using a sine series and a
wavelet expansion using 200 terms in the expansions.
![[Kuva]](fourex.png)
![[Kuva]](wavex.png)
Completion
You can complete the course by doing homework and taking part in the exam.
Study material
As the main study material lecture notes are used. They can be found
in PS and PDf form on the homepage
Literature:
-
I. Daubechies.
Ten lectures on wavelets.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992.
-
E. Hernández and G. Weiss.
A first course on wavelets.
CRC Press, Boca Raton, FL, 1996.
-
S. Jaffard, Y. Meyer, and R. D. Ryan.
Wavelets.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA,
revised edition, 2001.
-
A. Jensen and A. la Cour-Harbo.
Ripples in mathematics.
Springer-Verlag, Berlin, 2001.
-
S. Mallat.
A wavelet tour of signal processing.
Academic Press Inc., San Diego, CA, 1998.
-
Yves Meyer.
Ondelettes et opérateurs. I.
Hermann, Paris, 1990.
-
G. Strang and T. Nguyen.
Wavelets and filter banks.
Wellesley-Cambridge Press, Wellesley, MA, 1996.
Language
Finnish or english depending on the needs of the students
Teacher
The course is lectured by
Gustaf Gripenberg.
Infoemation
The information for the course is given on homepage
http://www.math.hut.fi/teaching/wavelet/ or by email.
Comments, questions!!!