Wavelet Analysis
The Scalable Structure of Information
(Sprache: Englisch)
This text gives a clear introduction to the ideas and methods of wavelet analysis, making concepts understandable by relating them to methods in mathematics and engineering. It shows how to apply wavelet analysis to digital signal processing and presents a wide variety of applications.
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This text gives a clear introduction to the ideas and methods of wavelet analysis, making concepts understandable by relating them to methods in mathematics and engineering. It shows how to apply wavelet analysis to digital signal processing and presents a wide variety of applications.
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.
Inhaltsverzeichnis zu „Wavelet Analysis “
Part I: The Scalable Structure of Information; 1. The New Mathematical Engineering;
2. Good Approximations;
3. Wavelets: A Positional Notation for Functions; Part 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; Part 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 Differentail Equations; Part IV: Wavelet Applications;
13. Wavelet Data Compression;
14. Modulation and Channel Coding; Bibliography.
Bibliographische Angaben
- Autoren: Howard L. Resnikoff , Raymond O.Jr. Wells
- 2002, 1st ed. 1998. Corr. 2nd printing 2002., 435 Seiten, 92 Abbildungen, Masse: 15,9 x 23,8 cm, Gebunden, Englisch
- Verlag: Springer, New York
- ISBN-10: 038798383X
- ISBN-13: 9780387983837
Sprache:
Englisch
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