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Lecture Notes

The lecture notes are available Initiates file downloadhere for download. The current version is from October 9th 2015.

Exam Preparation

Please have a look at Initiates file downloadthis document for some general remarks on oral exams, and a number of example questions. Note that this list is mainly intended to get an impression on what is expected from you. The questions in the exam may deviate from these examples.

Material

Material from the lecture, and supplementary material for a deeper understanding:

 

DateTopic
Oct. 14, 2015Initiates file downloadEinführende Notizen zu Fourierreihen (Introduction notes on Fourier series) - correction on Oct. 24
Initiates file downloadBeispiel zu Gibbs-Phänomen (Example on the Gibbs phenomenon)
Oct. 20, 2015Initiates file downloadTabelle zu Fourierreihen (Table on Fourier series)

Initiates file downloadBeispiele zu Fourierreihen (Examples on Fourier series)

Initiates file downloadZur linearen Algebra (Hilberträume) (On linear algebra (Hilbert spaces))
Oct. 21, 2015Initiates file downloadSchematische Übersicht zur DFT (Schematic overview on Discrete Fourier transform)
Initiates file downloadBeispiel zur DFT (Example on DFT)
Initiates file downloadFolien zur Haar-Transformation (Slides on the Haar transform) - correction on Oct. 28
Initiates file downloadBeispiele zur Haar-Transformation (Examples on Haar transform)
Initiates file downloadSchematische Übersicht zur HT (Schematic overview on Haar transform)
Nov. 3, 2015Initiates file downloadNotebook zu Anwendungen der Haar-Wavelet-Transformation (notebook on applications of the Haar wavelet transform)
Initiates file downloadWeiterführende Folien zur Haar-Transformation (Slides with additional information on the Haar transform)
Nov. 10, 2015Initiates file downloadFolien zur Schätzung der Haar-Koeffizienten (Slides on the estimation of Haar coefficients)
Initiates file downloadFolien zu Faltung, Korrelation und Z-Transformation (Slides on convolution, correlation and z-transform) - correction on Nov. 17
Initiates file downloadNotebook zur Schätzung der Haar-Koeffizienten (Notebook on the estimation of Haar coefficients)
Nov. 17, 2015Initiates file downloadFolien "Fourier Essentials" - von Fourier-Reihen zu Fourier Transformationen und weiteres (Fourier essentials - from Fourier series to Fourier transforms, and more) - correction on Nov. 18
Initiates file downloadNotebook mit Beispielen zur Fourier-Transormation (Notebook with examples on the Fourier transform)
Initiates file downloadNotebook mit Beispielen zur Filterung im Frequenzraum (Notebook with examples on filtering in frequency domain)
Initiates file downloadNotebook "Von Fourier-Reihen zur Fourier-Transformation" (Notebook "from Fourier series to Fourier transform)
Nov. 25, 2015Initiates file downloadNotebook mit Beispielen zu Sampling (Notebook with examples on sampling, undersampling, oversampling)
Initiates file downloadNotebook mit einer Demonstration des Sampling Theorems (Notebook with a demo on the sampling theorem)
Initiates file downloadFolien zu Signalen und Filtern (Slides on signals and filters)
Initiates file downloadNotebook zur diskreten Filterung von Signalen (Notebook on filtering discrete signals)
Initiates file downloadFolien zu orthogonalen Filtern und Rekonstruktion, Daubechies und Coiflet Filtern (Slides on orthogonal filters and reconstruction, Daubechies and Coiflet filters)
Dec. 1, 2015Initiates file downloadZusammenfassung zu diskreten Wavelet-Transformationen (Synopsis on discrete wavelet transforms)
Initiates file downloadNotebook zur Konstruktion von D4- und D6-Filtern (Notebook on the construction of D4 and D6 filters)
Initiates file downloadNotebook zur Konstruktion von C6-Filtern (Notebook on the construction of C6 filters)
Initiates file downloadNotebook zu Filtern und Matrizen aller bisher betrachteter Filter (Notebook on filters and matrices of all currently considered filters)
Dec. 2, 2015Initiates file downloadFolien "From filters to scaling and wavelet functions via the cascade algorithm or via dyadic interpolation" (Slides)
Initiates file downloadNotebook zur Approximation von Scaling- und Wavelet-Funktionen mit dem Cascade-Algorithmus (Notebook on approximation of scaling and wavelet functions using the cascade algorithm)
Initiates file downloadNotebook zur dyadischen Approximation von Scaling- und Wavelet-Funktionen (Notebook on dyadic approximation of the scaling and wavelet functions)
Initiates file downloadNotebook zur Energiekonzentration in der DWT (Notebook on concentration of energy in DWT)
Dec. 9, 2015Initiates file downloadSlides "A closer look at the cascade algorithm: convergence, compact support, reproducing polynomials, vanishing moments"
Initiates file downloadWorksheet "Approximation of polynomial functions by wavelet scaling functions (vanishing moments)"
Dec. 15, 2015Initiates file downloadNotebook "Concentration of Energy by DWT"
Initiates file downloadSlides "Multiresolution Analysis (MRA)"
Initiates file downloadA synopsis on the mathematical properties of multiresolution analysis
Dec. 17, 2015Initiates file downloadRemarks on embedded trees in DWT data
Initiates file downloadNotebook "Embedded trees for 1-D DWT"
Dec. 22, 2015Initiates file downloadSlides "Denoising using wavelets"
Initiates file downloadNotebook "Denoising using wavelets" (part 1)
Initiates file downloadNotebook "Example for image denoising using wavelets" (part 2)
Initiates file downloadNotebook "Example for image denoising using wavelets" (part 3)
Initiates file downloadNotebook "1-D examples for image denoising using wavelets" (part 4)
Jan. 13, 2016Initiates file downloadDWT, embedded trees, progressive transmission, and the SPIHT algorithm
Jan. 19, 2016Initiates file downloadNotebook on bit approximation
Initiates file downloadNotebook on SPIHT examples - correction (II) on Jan. 20
Initiates file downloadOverview page on the SPIHT bitstream
Initiates file downloadOverview page on the tree decomposition
Jan. 20, 2016Initiates file downloadImplementation of the SPIHT procedures
Initiates file downloadSlides on Biorthogonal Filter Pairs and Wavelets
Jan. 27, 2016Initiates file downloadSlides on constructing biorthogonal filter pairs
Initiates file downloadNotebook on biorthogonal filter pairs (B-splines, CDF-7/9)
Initiates file downloadNotebook on discrete approximation of derivatives and the influence of noise and rounding errors
Feb. 2, 2016Initiates file downloadNotebook "Illustrating the Continuous Wavelet Transform (CWT)"
Initiates file downloadSlides on Continuous wavelet transform and edge detection
Initiates file downloadNotebook "Illustrating the a-trous algorithm"
Initiates file downloadSlides on Wavelets and edge detection
Initiates file downloadNotebook "Edge detection using the Sobel operators"
Initiates file downloadNotebook "Edge detection using wavelets"
Initiates file downloadNotebook "Illustrating edge detection"

 

 

More material can be found at the Opens external link in new windowlecture page from the previous year.

Selected Literature

  • J. Bergh, F. Ekstedt, M. Lindberg: Wavelets mit Anwendungen in der Signal- und Bildverarbeitung, Springer, 2007.
  • A. Bogess, F. J. Narcowich: A First Course in Wavelets with Fourier Analysis, Prentice Hall, 2001.
  • A. Jaffard, Y. Meyer, R. D. Ryan: Wavelets, Tools for Science & Technology, SIAM, 2001.
  • Y. Nievergelt: Wavelets Made Easy, Birkhäuser, 1999.
  • R. M. Rao, A. S. Bopardikar: Wavelet Transforms, Addison-Wesley, 1998.
  • J. S. Walker: A Primer on Wavelets and their Scientific Applications, Chapman & Hall, 1999.
  • D. F. Walnut: An Introduction to Wavelet Analysis, Birkhäuser, 2002.