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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 [13] 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 [26].
Extensive literature exists on the Wavelet Transform and its
applications
([#chui<#14223,#daube<#14224,#meyer90<#14225,#meyer92<#14226,#meyer91<#14227,#ruskai<#14228]). We
summarize the main features here.

*Petra Nass*

*1999-06-15*