Stefan,
The analogy with Fourier transforms was the original
motivation. The primary difference between a wavelet
and a sine wave (or cosine wave) is that sine waves
extend to infinity in both directions, but a wavelet
is zero except on a finite interval.
> I've always been thinking of wavelet transforms as
> a "variant" of Fourier transformation, which is also
> (at least supposed to be) invertible in the continuous
> case.
The property of being invertible is central to the
definition of wavelet transforms. Extending continuous
methods to discrete structures, such as words and texts,
introduces difficulties, but the possibility of finding
an inverse is highly desirable whenever possible. In
some cases, the inverse is "lossy" -- i.e., much of the
original detail is lost in the reconstruction.
John Sowa
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