MAA603 Wavelets

Wavelets play an essential role in modern signal processing and appear in many applications in electromagnetism, scattering, image analysis and acoustics.
In this course it will be described how to use the short-time Fourier transform to gain information about both the time domain and frequency domain, use the continuous wavelet transform to analyze signals with both slow and fast rate of change, and several different methods and concepts for analyzing and recreating signals such as multiresolution analysis, Daubechies orthonormal wavelet bases and more.

Course information

Course syllabus

Course study guide

MAA603 Wavelets, course study guide (pdf 38 kB)

Recommended course materials, online resourses and literature

Introduction to Transform Theory with Applications.

This is an excellent introductory repetition material reviewing in concrete and practical way standard transforms such as Laplace transform (LP), Fourier transform (FT), discrete FT, wavelet transform and more.  

Chapter 6 from A Basic Course in Applied Mathematics   by Prof. Lars-Erik Persson

 

Basics of Wavelets tutorial by Mark Kon

Basics of Wavelets tutorial by Mark Kon

Basics of Wavelets tutorial by Mark Kon (pdf 1.1 MB)

Mark Kon's Wavelets lectures slides and other relevant course materials 

 

Wavelets, Filter Banks and Applications

Gilbert Strang, and Kevin Amaratunga. (MIT course number 18.327) 

Wavelets, Filter Banks and Applications, Spring 2003.

Massachusetts Institute of Technology: MIT OpenCourseWare  http://ocw.mit.edu http://ocw.mit.eduhttp://ocw.mit.eduhttp://ocw.mit.eduhttp://ocw.mit.eduhttp://ocw.mit.eduhttp://ocw.mit.eduhttp://ocw.mit.eduhttp://ocw.mit.eduhttp://ocw.mit.edu

License: Creative Commons BY-NC-SA

http://ocw.mit.edu/courses/mathematics/18-327-wavelets-filter-banks-and-applications-spring-2003/index.htm#

 

Wavelets toure of Signal processing

by  Stéphane Mallat

A wavelet tutorial adapted for the web 

Links to websites for this excellent book several editions with usefull suplementary resources, numerical wavelets software and links:

A Wavelet Tour of Signal Processing, 3rd edition

A Wavelet Tour of Signal Processing, 2nd Edition

Other recommended resources and literature on Wavelets

Wavelets, Spring 2014. 

PhD (post-graduate) education level course Wavelets was given for the first time at Mälardalen University by  Professor Anatoliy Malyarenko in Spring 2014 

Lecture notes/slides of the lectures by Anatoliy Malyarenko:  

Lecture 1 (pdf 158 kB)

Lecture 2 (pdf 122 kB)

Lecture 3 (pdf 149 kB)

Lecture 4 (pdf 167 kB)

Lecture 5 (pdf 130 kB)

Lecture 6 (pdf 148 kB)

Lecture 7 (pdf 167 kB)

Lecture 8 (pdf 136 kB)

Book by Professor Palle Jorgensen from University of Iowa, USA

Analysis and Probability: Wavelets, Signals, Fractals

by   Palle E. T. Jorgensen

Graduate Texts in Mathematics, Vol. 234, Springer

 

Usefull online resourses on Wavelets: 

Wavelets digest

Youtube open access lectures on Wavelets: 

Professor Ole Christensen, DTU (Technical University of Denmark)

Fourier Transform and Wavelets Part 1

(Note: Part 1 of this lecture is mostly about Fourier Transform and convolution properties only with no wavelets involved. Thus, one can start from Part 2 directly concerned with Wavelets.)

Fourier Transform and Wavelets Part 2

Wavelets and Multiresolution analysis. Part 1

Wavelets and Multiresolution Analysis. Part 2

Course responsible

Examiner: Professor Sergei Silvestrov