For many years, digital signal processing has been governed by the
theory of Fourier transform and its numerical implementation. The
main disadvantage of Fourier theory is the underlying assumption
that the signals have time-wise or space-wise invariant statistical
properties. In many applications the deviation from a stationary
behavior is precisely the information to be extracted from the
signals. Wavelets were developed to serve the purpose of analysing
such instationary signals. The book gives an introduction to
wavelet theory both in the continuous and the discrete case. After
developing the theoretical fundament, typical examples of wavelet
analysis in the Geosciences are presented. The book has developed
from a graduate course held at The University of Calgary and is
directed to graduate students who are interested in digital signal
processing. The reader is assumed to have a mathematical background
on the graduate level.
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