Wavelets in Geodesy and Geodynamics

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Overview

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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Product Details

  • ISBN-13: 9783110175462
  • Publisher: De Gruyter, Walter, Inc.
  • Publication date: 4/28/2004
  • Pages: 279
  • Product dimensions: 6.90 (w) x 9.68 (h) x 0.81 (d)

Table of Contents

1 Fourier analysis and filtering 1
2 Wavelets 24
2.1 Motivation 24
2.2 Continuous wavelet transformation 30
2.3 Discrete wavelet transformation 40
2.4 Multi-resolution analysis 43
2.5 Mallat algorithm 55
2.6 Wavelet packages 63
2.7 Biorthogonal wavelets 68
2.8 Compactly supported orthogonal wavelets 82
2.9 Wavelet bases on an interval 98
2.10 Two-dimensional wavelets 102
2.11 Wavelets on a sphere 110
3 Applications 131
3.1 Pattern recognition 131
3.2 Data compression and denoising 156
3.3 Sub-band coding, filtering and prediction 181
3.4 Operator approximation 196
3.5 Gravity field modelling 212
A Hilbert spaces 217
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