Wavelets in Geodesy and Geodynamics

Wavelets in Geodesy and Geodynamics

by Wolfgang Keller
     
 

ISBN-10: 3110175460

ISBN-13: 9783110175462

Pub. Date: 04/28/2004

Publisher: De Gruyter, Walter, Inc.

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

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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:
04/28/2004
Pages:
279
Product dimensions:
6.90(w) x 9.68(h) x 0.81(d)
Age Range:
18 Years

Table of Contents

1Fourier analysis and filtering1
2Wavelets24
2.1Motivation24
2.2Continuous wavelet transformation30
2.3Discrete wavelet transformation40
2.4Multi-resolution analysis43
2.5Mallat algorithm55
2.6Wavelet packages63
2.7Biorthogonal wavelets68
2.8Compactly supported orthogonal wavelets82
2.9Wavelet bases on an interval98
2.10Two-dimensional wavelets102
2.11Wavelets on a sphere110
3Applications131
3.1Pattern recognition131
3.2Data compression and denoising156
3.3Sub-band coding, filtering and prediction181
3.4Operator approximation196
3.5Gravity field modelling212
AHilbert spaces217

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