Wavelets: The Key to Intermittent Information?

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Oxford University Press, 2000 - Mathematics - 256 pages
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In recent years there has been an explosion of interest in wavelets, in a wide range of fields in science and engineering and beyond. This book brings together contributions from researchers from disparate fields, both in order to demonstrate to a wide readership the current breadth of work in wavelets, and to encourage cross-fertilization of ideas. It demonstrates the genuinely interdisplinary nature of wavelet research and applications. Particular areas covered include turbulence, statistics, time series analysis, signal and image processing, the physiology of vision, astronomy, economics and acoustics. Some of the work uses standard wavelet approaches and in other cases new methodology is developed. The papers were originally presented at a Royal Society Discussion Meeting, to a large and enthusiastic audience of specialists and non-specialists.
 

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Contents

Wavelets in timeseries analysis
1
The onedimensional case
7
Applications
16
Experimental evidence for lognormal statistics
25
Experimental evidence for a nonscaleinvariant lognormal
32
The multifractal description of intermittency revisited with wavelets
38
Conclusions and perspectives
44
Intermittency and eddy capacity
50
Dealing with irregular data
77
Acknowledgements
85
Optimality in the whitenoise model
99
The continuous ridgelet transform
115
Wavelets vision and the statistics of natural scenes
149
Image processing with complex wavelets
165
Approximation and compression of piecewise smooth functions
199
2 The contribution of wavelets to the analysis of economic
221

Application to high resolution turbulent velocity signals
63
References
70
3 Harmonic wavelets in vibrations and acoustics
237
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About the author (2000)

B. W. Silverman is in the School of Mathematics at University of Bristol. J. C. Vassilicos is in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge.

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