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Title

Wavelets: An Introduction
Author

Paul Abbott
Organization: University of Western Australia
Department: Physics
URL: http://www.physics.uwa.edu.au/~paul
Education level

College
Objectives

Broadly speaking, wavelets and Fourier methods have similar areas of application. One motivation for the development of wavelets was to overcome deficiencies with Fourier methods. Basically, because Fourier methods analyse signals using a periodic basis, they are not well adapted to signals that have finite (spatial or temporal) duration.

This course is a brief introduction to wavelets and is not overly mathematical. The basic mathematical tools required are quite simple: basic calculus, eigenvalues and eigenvectors, and recursive equations.
Materials

Recommended reading:
  • Wavelets: An Elementary Treatment of Theory and Applications by Koornwinder (University of Amsterdam)
  • Vol 1 in: Series in Approximations & Decompositions by Chui, series editor (World Scientific, 1993)
Description

All students taking this course use Mathematica to complete the exam.

Topics:
  • Introduction
  • Mathematical preliminaries
  • The continuous wavelet transform
  • Discrete wavelets and multiresolution analysis
  • Applications -- Signal denoising and image compression using wavelets
Subject

*Applied Mathematics > Numerical Methods > Approximation Theory > Wavelets
URL

http://physics.uwa.edu.au/information_for/current/honours/modules/wavelets