The course aims at giving a mathematically coherent introduction into the theory of wavelets and the connections with signal analysis. The following topics are included: Fourier series, Fourier transform (including Shannon’s sampling theorem), Windowed Fourier Transform, Continuous Wavelet Transform, Frames, Discrete Wavelet Transform, Multi Resolution Analysis, Orthonormal wavelet bases, Construction of Wavelets. After the course the student will be able to explain the basic aspects of the theory of wavelets, and to read the literature on the subject.
Prerequisites
Some basic knowledge of Hilbert spaces and measure and integration theory.
Literature
Christian Blatter, Wavelets: a primer, A.K. Peters, Nateck, USA, 1998; [ISBN 1-56881-4]
Course code TU Delft
WI4005
Assessment
Take-home exercises and oral examination
Contact
2 hours lectures per week
Remark
This course can be part of a Leiden master’s programme