M8181 Wavelet Analysis

Faculty of Science
Spring 2010
Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Kolář, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 13:00–14:50 01031
Prerequisites (in Czech)
M4170 Measure and Integral && M6150 Linear Functional Analysis I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
At the end of the course students should be able to: understand and explain basic techniques for analysis of time series using wavelets and filters, define discrete and continuous wavelet transforms, prove main results of multiresolution analysis, use various types of finite filters.
Syllabus
  • Continuous wavelet transform
  • The Calderon identity
  • Discrete wavelet transform
  • Filter banks
  • Lowpass a highpass filters
  • Multiresolution analysis
  • Orthonormal filters
  • Relations between filters a wavelets
  • Daubechies filter and wavelet
Literature
  • STRANG, Gilbert and Truong NGUYEN. Wavelets and filter banks. Wellesley: Wellesley-Cambridge Press, 1996, 490 s. ISBN 0-9614088-7-1. info
  • MEYER, Yves. Wavelets :algorithms and applications. Translated by Robert D. Ryan. Philadelphia: Society for Industrial and Applied Mathematics, 1993, 133 s. ISBN 0-89871-309-9. info
  • CHUI, C. K. In introduction to wavelets. San Diego: Academic Press, 1992, 267 s. ISBN 0121745848. info
  • DAUBECHIES, Ingrid. Ten lectures on wavelets. Philadelphia, Pa.: Society for Industrial and Applied Mathematics, 1992, xix, 357 s. ISBN 0-89871-274-2. info
  • MEYER, Yves. Wavelets and operators. Edited by D. J. H. Garling, Translated by D. H. Salinger. Cambridge: Cambridge University Press, 1992, 223 s. ISBN 0521420008. info
Teaching methods
Lectures, 2 hours per week
Assessment methods
Oral exam
Language of instruction
Czech
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2008.
  • Enrolment Statistics (recent)
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