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MA7521 Wavelets and Signal Processing

MA7521 Wavelets and Signal Processing

Credits: 15 Convenor: Dr J. Levesley Semester: 2
Prerequisites:
Assessment: Fortnightly work, computer practicals, project: 50% 3 hour examination: 50%
Lectures: 36 Problem Classes: 10
Tutorials: none Private Study: 94
Labs: 10 Seminars: none
Project: none Other: none
Surgeries: 0 Total: 150

Subject Knowledge

Aims

This module aims to show students how to use wavelets to analyse and compress signals. The tools of Fourier analysis will be developed to give a theoretical understanding of wavelet approximation. Students will also learn, via computer practicals, to actually analyse and compress digital signals.

Learning Outcomes

To learn basic harmonic analysis, to understand and apply the idea of a filter bank, to learn the mathematical and computational theory of wavelets, to be able to analyse and compress a signal using wavelets.

Methods

Lectures, computer practicals.

Assessment

Marked fortnightly work, project reports, practical diaries, examination.

Subject Skills

Aims

To provide students with report writing, oral communication and IT skills.

Learning Outcomes

Students write a project reports, keep a practical log, and give an oral project presentation. They will do computer lab work.

Methods

Workshops, computer proacticals.

Assessment

Project report, project presentation, and practical diary.

Explanation of Pre-requisites

Course Description

Wavelets are very useful tools for data analysis and compression. Current research into the uses of wavelets for these and other purposes is intense. In this course you will be introduced to the mathematical theory of wavelets. One of the key tools here is harmonic analysis, which is a very useful tool in a variety of settings. You will also learn, in a practical setting, how to use wavelets to analyse and compress digital signals.

Syllabus

Filter banks. The basic space $L^2(R)$ and the basic facts we need to know about it. Results about the Fourier transform, including Parseval's identity. Brief discussion of Fourier series. Introduction to wavelets, the Haar wavelet as an elementary model example, the two-scale equation, multiresolution analysis, how the multiresolution analysis aids the construction of wavelets, stable bases in $L^2(R)$, the decomposition and reconstruction algorithms, the symbol, compactly supported wavelets, the cascade algorithm for constructing wavelets from the two scale equation.

Reading list

Background:

E.W. Cheney and W.A. Light, A Course in Approximation Theory, Brooks Cole, 2000.

J. Prestin, in, Tutorials on Multiresolution in Geometric Modelling, (Iske et. al. (eds)), Springer-Verlag, 2002.

G. Strang, in, Wavelets, Multilevel Methods and Elliptic PDE's, (Ainsworth et. al. (eds)), OUP, 1997.

C. K. Chui, An Introduction to Wavelets, Academic Press, 1992.

Resources

Computer laboratories, lecture rooms.

Module Evaluation

Module questionnaires, module review, course review.

Next: MA7541 Methods in Molecular Simulation Up: ModuleGuide03-04 Previous: MA7511 Finite Element Methods for Partial

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