<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <!--Converted with LaTeX2HTML 98.1p1 release (March 2nd, 1998) originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds * revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan * with significant contributions from: Jens Lippmann, Marek Rouchal, Martin Wilck and others --> <HTML> <HEAD> <TITLE>Introduction</TITLE> <META NAME="description" CONTENT="Introduction"> <META NAME="keywords" CONTENT="vol2"> <META NAME="resource-type" CONTENT="document"> <META NAME="distribution" CONTENT="global"> <META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"> <LINK REL="STYLESHEET" HREF="vol2.css"> <LINK REL="next" HREF="node310.html"> <LINK REL="previous" HREF="node308.html"> <LINK REL="up" HREF="node308.html"> <LINK REL="next" HREF="node310.html"> </HEAD> <BODY > <!--Navigation Panel--> <A NAME="tex2html5324" HREF="node310.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="icons.gif/next_motif.gif"></A> <A NAME="tex2html5321" HREF="node308.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="icons.gif/up_motif.gif"></A> <A NAME="tex2html5315" HREF="node308.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="icons.gif/previous_motif.gif"></A> <A NAME="tex2html5323" HREF="node1.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="icons.gif/contents_motif.gif"></A> <BR> <B> Next:</B> <A NAME="tex2html5325" HREF="node310.html">The continuous wavelet transform</A> <B> Up:</B> <A NAME="tex2html5322" HREF="node308.html">The Wavelet Transform</A> <B> Previous:</B> <A NAME="tex2html5316" HREF="node308.html">The Wavelet Transform</A> <BR> <BR> <!--End of Navigation Panel--> <H1><A NAME="SECTION002010000000000000000"> Introduction</A> </H1> The Fourier transform is a tool widely used for many scientific purposes, but it is well suited only to the study of stationary signals where all frequencies have an infinite coherence time. The Fourier analysis brings only global information which is not sufficient to detect compact patterns. Gabor [<A HREF="node370.html#gabor">13</A>] introduced a local Fourier analysis, taking into account a sliding window, leading to a time frequency-analysis. This method is only applicable to situations where the coherence time is independent of the frequency. This is the case for instance for singing signals which have their coherence time determined by the geometry of the oral cavity. Morlet introduced the Wavelet Transform in order to have a coherence time proportional to the period [<A HREF="node370.html#meyer">26</A>]. <P> Extensive literature exists on the Wavelet Transform and its applications ([#chui<#14223<A HREF="node370.html#>"></A>,#daube<#14224<A HREF="node370.html#>"></A>,#meyer90<#14225<A HREF="node370.html#>"></A>,#meyer92<#14226<A HREF="node370.html#>"></A>,#meyer91<#14227<A HREF="node370.html#>"></A>,#ruskai<#14228<A HREF="node370.html#>"></A>]). We summarize the main features here. <P> <BR><HR> <ADDRESS> <I>Petra Nass</I> <BR><I>1999-06-15</I> </ADDRESS> </BODY> </HTML>
