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<H2><FONT size=8>A</FONT>n <FONT size=8>I</FONT>ntroduction to <FONT
size=8>W</FONT>avelets</H2>
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<H3>Abstract</H3><ABSTRACT>Wavelets are mathematical functions that cut up
data into different frequency components, and then study each component with a
resolution matched to its scale. They have advantages over traditional Fourier
methods in analyzing physical situations where the signal contains
discontinuities and sharp spikes. Wavelets were developed independently in the
fields of mathematics, quantum physics, electrical engineering, and seismic
geology. Interchanges between these fields during the last ten years have led
to many new wavelet applications such as image compression, turbulence, human
vision, radar, and earthquake prediction. This paper introduces wavelets to
the interested technical person outside of the digital signal processing
field. I describe the history of wavelets beginning with Fourier, compare
wavelet transforms with Fourier transforms, state properties and other special
aspects of wavelets, and finish with some interesting applications such as
image compression, musical tones, and de-noising noisy data.
<P>Keywords: Wavelets, Signal Processing Algorithms, Orthogonal Basis
Functions, Wavelet Applications </ABSTRACT>
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<H3>Contents:</H3>
<OL>
<LI><A href="http://www.amara.com/IEEEwave/IW_overview.html">Overview</A>
<BR><BR>
<LI><A href="http://www.amara.com/IEEEwave/IW_history.html">Historical
Perspective</A> <BR><BR>
<LI><A href="http://www.amara.com/IEEEwave/IW_basis.html">Sidebar- What are
Basis Functions?</A> <BR><BR>
<LI><A href="http://www.amara.com/IEEEwave/IW_fourier_ana.html">Fourier
Analysis</A> <BR><BR>
<LI><A href="http://www.amara.com/IEEEwave/IW_wave_vs_four.html">Wavelet
Transforms versus Fourier Transforms</A> <BR><BR>
<LI><A href="http://www.amara.com/IEEEwave/IW_see_wave.html">What Do Some
Wavelets Look Like?</A> <BR><BR>
<LI><A href="http://www.amara.com/IEEEwave/IW_wave_ana.html">Wavelet
Analysis</A> <BR><BR>
<LI><B>Wavelet Applications</B></A>
<P>
<UL>
<LI><A href="http://www.amara.com/IEEEwave/IW_vision.html">Computer and
Human Vision</A> <BR><BR>
<LI><A href="http://www.amara.com/IEEEwave/IW_fbi.html">FBI Fingerprint
Compression</A> <BR><BR>
<LI><A href="http://www.amara.com/IEEEwave/IW_denoising.html">Denoising
Noisy Data</A> <BR><BR>
<LI><A href="http://www.amara.com/IEEEwave/IW_selfsim.html">Detecting
Self-Similarity in a Time Series</A> <BR><BR>
<LI><A href="http://www.amara.com/IEEEwave/IW_musicaltones.html">Musical
Tones</A> </LI></UL><BR>
<LI><A href="http://www.amara.com/IEEEwave/IW_endnote.html">Wavelets
Endnote</A> <BR><BR>
<LI><A href="http://www.amara.com/IEEEwave/IW_ref.html">References</A>
</LI></OL>
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<H4>To Download This Paper:</H4>
<P>Press <A href="http://www.amara.com/ftpstuff/IEEEwavelet.ps.gz">HERE </A>to
FTP a gzipped, postscript copy. (800 Kbytes compressed, gunzips to 2.6
Mbytes).
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<H4>Copyright Notice</H4>
<H6>Copyright (c) 1995 by the Institute of Electrical and Electronics
Engineers, Inc. Personal use of this material is permitted. However,
permission to reprint/republish this material in digital or hard copy form
must be obtained from the IEEE. To copy or otherwise, to republish, to post on
servers, to redistribute to lists, or to use any component of this work in
other works for any purpose requires prior permission from the IEEE. A fee may
be charged for re-use. Abstracting with credit is permitted. Copyrights for
components of this work owned by others than IEEE must be honored.
<P>The original version of this work appears in IEEE Computational Science and
Engineering, Summer 1995, vol. 2, num. 2, published by the IEEE Computer
Society, 10662 Los Vaqueros Circle, Los Alamitos, CA 90720, USA, TEL
+1-714-821-8380, FAX +1-714-821-4010. </H6>
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<ADDRESS>Last Modified by <A href="mailto:amara@amara.com">Amara
Graps</A> on 8 October 1997.<BR>© Copyright Amara Graps, 1995-1997.
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