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Session 1320

Combining Wavelets in a Digital Signal Processing Course

Sol Neeman Johnson and Wales University

Abstract

Waveletsis a relatively new topic in engineeringand computerscience. Some of its applicationsare in the area of digital signal processing. This paper suggeststo integratea sessionin a digital signalprocessingclass at an un- dergraduate level that wouldexpcee studentsto some of the basic topics of the Wavelet Transform and its applications the analysisof signals(e.g. de- in tectionof discontinuity, detectionof self sin&&y and denoisingof signals) as well as image compmssion.This would enhance the DSP class and enrich studentsview of the time - frequency relations.

Introduction

A sessionon the Wavelet ‘ Ikansform a DSP courseshould presentthe in topic in the context of tim&equency representation signals. Probably of the meet naturalpoint to start with is periodicsignals,where the most nat- ural tool for their representation would be the Fourier%x-i-. It will provide the amplitudesof the frequency componentsof the signal, the fundamental ,_ frequency and.ite harmonica.In the case of non-periodic signals, we can ap _ ‘ .~ : .-&&cit&j jjlourier_.Integral. j&Q& it&* so-&n && &e fFequnncy

:. ~:~e&3 con@&gthesignal,.thistransformdoesnotprovideinf~ c tion on the tim&equency relationsin the s@aL The Fhrier ‘ Ikansform does not provideinformationthat would let us associatecertainevents (e.g. abrupt changes,long term behaviorof a s&al) with certain points of time. , TlG3 presentationc811providea motivationfor the Wavelet Tkansform.

The Windowed Fourier lhmsform( WFT) A partialsolutionto the above problemwouldbe to partitionthe signal into sections (the width of which depends on the application), then apply the Fourier‘Ikansform each piece. This is the Windowed Fourier‘ to Ikans- form(WF”T). Clearly questionsregardingwhen a section should begin and

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Neeman, S. (1999, June), Combining Wavelets In A Digital Signal Processing Course Paper presented at 1999 Annual Conference, Charlotte, North Carolina. 10.18260/1-2--8105