Wavelet Analysis
The Scalable Structure of Information
1st ed. 1998. Corr. 2nd printing 2001. XVI, 435 pp. 92 figs. Hardcover 0-387-98383-X
The past decade has witnessed the rapid development of a new
mathematical tool, called wavlet analysis, for analyzing complex signals. It
has begin to play a serious role in applications ranging from
communications to geophysics, and from simulations to image processing.
Like Fourier analysis (of which it is a generalization), or musical notation,
wavelet analysis provides a method for representing a set of complex
phenomena in a simpler, more compact, and thus more efficient manner.
This text introduces the ideas and methods of wavelet analysis, relates
them to previously known methods in mathematics and engineering, and
shows how to apply wavelet analysis to digital signal processing. It begins
by describing the multiscale (sometimes called "fractal") nature of
information in many aspects of the real world; it then turns to the algebra
and analysis of wavelet matrices, scaling and wavelet functions, and the
corresponding analysis of square-integrable functions on a space. The
discussion then turns from the continuous to the discrete and shows how a
properly selected set of wavelets can be used to represent -- and even
differentiate -- a wide range of signls efficiently and effectively. The last part
of the book presents a wide variety of applications of wavelets to probllems
in data compression and telecommunications.
TOC
Preface
I: The Scalable Structure of Information
1: The New Mathematical Engineering
2: Good Approximations
3: Wavelets: A Positional Notation for Functions
II: Wavelet Theory
4: Algebra and Geometry of Wavelet Matrices
5: One-Dimensional Wavelet Systems
6: Examples of One-Dimensional Wavelet Systems
7: Higher-Dimensional Wavelet Systems
III: Wavelet Approximation and Algorithms
8: The Mallat Algorithm
9: Wavelet Approximation
10: Wavelet Calculus and Connection Coefficients
11: Multiscale Representation of Geometry
12: Wavelet-Galerkin Solutions of Partial Differential Equations
IV: Wavelet Applications
13: Wavelet Data Compression
14: Modulation and Channel Coding
References
Index