Wavelet analysis had its origins in the mid-eighties. From the very beginning it was driven by application needs: The desire to analyze seismic signals more sensitively than with Fourier techniques led to the first appearance of the continuous wavelet transform formula. In parallel it turned out that the new technique could be applied successfully to certain problems in theoretical
physics as well as in pure mathematics. For one of the earliest collections of research and survey papers documenting the state of the art the reader is
referred to [6].
It soon turned out that wavelet analysis successfully could be applied to many types of signal processing problems: In signal analysis the detection
of discontinuities or irregularities was tackled with wavelets. The analysis of
medical signals like electrocardiograms of the heart is one of the first reported
examples of discontinuity detection (see [6]). For more applications, like the
analysis of sensor signals in robotics, cf. sect. 2.3.1.