Course Wavelets
Responsible: Prof.Dr. Alexander Stoffel
Course
Meets requirements of following modules(MID)
Course Organization
Version 

created 
20130429 
VID 
2 
valid from 
WS 2012/13 
valid to 



Course identifiers 

Long name 
Wavelets 
CID 
F07_WL 
CEID (exam identifier) 


Contact hours per week (SWS) 

Lecture 
2 
Exercise (unsplit) 
1 
Exercise (split) 

Lab 
1 
Project 

Seminar 

Tutorial(voluntary) 



Total contact hours 

Lecture 
30 
Exercise (unsplit) 
15 
Exercise (split) 

Lab 
15 
Project 

Seminar 

Tutorial (voluntary) 



Max. capacity 

Exercise (unsplit) 

Exercise (split) 

Lab 
30 
Project 

Seminar 


Total effort (hours): 150
Instruction language
 english (german only if whole auditory is german speaking)
Study Level
Prerequisites
 first year undergraduate mathematics course
 basic knowledge of digital signal processing, in particular concerning the ztransform
 basic experience in programming
Textbooks, Recommended Reading
 Strang, Gilbert; Nguyen Truong: Wavelets and Filter Banks
 C. Sidney Burrus; Ramesh A. Gopinath; Haitao Guo: Introduction to Wavelets and Wavelet Transforms. A Primer
 Bäni, Werner: Wavelets. Eine Einführung für Ingenieure
Instructors
 Prof.Dr. Alexander Stoffel
Supporting Scientific Staff
Transcipt Entry
Wavelets
Assessment
Type 

oE 
oral examen 
oR 
no 
Total effort [hours] 

sMP 
10 
Frequency: 2/year
Course components
Lecture/Exercise
Objectives
Contents
 wavelets and filter banks: analogy to Fourier series, the Haar wavelet and its filter bank, description of filters by impulse response, ztransform and matrices, subsampling and upsampling
 twochannel filter bank, condition of perfect reconstruction, quality considerations
 construction of appropriate filters, construction of the corresponding scaling function and wavelet
 the lifting scheme, DeslauriersDubucfilters
 denoising and image compression
Acquired Skills
 The students know what wavelet and Fourier transform have in common and what the differences are. They are able to describe simple filters by the impulse response and the ztransform and to calculate the corresponding matrix.
 They are able to explain filter banks using the example of the Haar filter bank. They know the quality criteria for filter banks and are able to explain the disadvantages of the Haar wavelet.
 They know the method to construct filters for biorthogonal wavelets and are able to give the most important examples.
 The students are able to explain the lifting scheme using the example of the lazy wavelet and the hat wavelet. They are able to explain the corresponding generalisation to DeslauriersDubucFilters.
 The students understand simple algorithms for denoising and data compression using wavelets. They are able to explain advantages and disadvantages of different wavelets for those applications.
Operational Competences
 The students are able to implement simple programs in Scilab to visualize advantages and disadvantages of different wavelet transforms and to illustrate calculation schemes.
Additional Component Assessment
Lab
Objectives
Contents
 influence of quantization errors at the reconstruction of image data from their coefficients, importance of vanishing moments for data compression
 denoising algorithms for audio data
 comparison of different thresholding algorithms for denoising image data
 coding experiments for wavelet coefficients to achieve data compression
Acquired Skills
 The students are able to implement a Scilab program which visualizes the influence of quantization errors at the reconstruction of image data. They are able to draw conclusions on the properties of scaling functions and wavelets. Furthermore they are able to implement a program for determining the number of vanishing moments and they explain the importance of the number of vanishing moments for data compression using example signals.
 The students are able to implement a Scilab program which tests denoising algorithms for one dimensional signals and visualizes the results. They extend this program to denoise an audio signal and optimize the result by varying the value of the threshold.
 The students are able to implement a Scilab program which tests different thresholding algorithms for denoising of image data. They analyze the results concerning the quality of the denoised images.
 The students implement a Scilab program for experiments with coding algorithms for wavelet coefficients and subsequent data compression. They compare and interprete the practical results using different wavelet transforms for image compression.
Operational Competences
 The students are able to implement Scilab programs which test and compare the quality of different wavelet transforms in view of practical applications. They document the results of such tests and explain them to other students.
Additional Component Assessment
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