Multiscale Analysis of Complex Time Series
Integration of Chaos and Random Fractal Theory, and Beyond
1. Edition October 2007
368 Pages, Hardcover
Wiley & Sons Ltd
Short Description
Signal Processing with Random Fractals introduces a number of key concepts from random fractal theory by emphasizing their usage in signal processing. A number of applications are discussed in depth. These include DNA sequence analysis, network traffic modeling, analysis of neuron inter-spike interval data, and study of heart rate variability and ambiguous visual perception.
The only integrative approach to chaos and random fractal theory
Chaos and random fractal theory are two of the most important theories developed for data analysis. Until now, there has been no single book that encompasses all of the basic concepts necessary for researchers to fully understand the ever-expanding literature and apply novel methods to effectively solve their signal processing problems. Multiscale Analysis of Complex Time Series fills this pressing need by presenting chaos and random fractal theory in a unified manner.
Adopting a data-driven approach, the book covers:
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DNA sequence analysis
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EEG analysis
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Heart rate variability analysis
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Neural information processing
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Network traffic modeling
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Economic time series analysis
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And more
Additionally, the book illustrates almost every concept presented through applications and a dedicated Web site is available with source codes written in various languages, including Java, Fortran, C, and MATLAB, together with some simulated and experimental data. The only modern treatment of signal processing with chaos and random fractals unified, this is an essential book for researchers and graduate students in electrical engineering, computer science, bioengineering, and many other fields.
1. Introduction.
2. Overview of fractal and chaos theory.
3. Basics of probability theory and stochastic processes.
transform, and probability generating function.
4. Fourier analysis and wavelet multiresolution analysis.
5. Basics of fractal geometry.
6. Self-similar stochastic processes.
7. Stable laws and Levy motions.
8. Long memory processes and structure-function-based multifractal analysis.
9. Multiplicative multifractals.
10. Stage-dependent multiplicative processes.
11. Models of power-law-type behavior.
12. Bifurcation theory.
13. Chaotic time series analysis.
14. Power-law sensitivity to initial conditions (PSIC).
15. Multiscale analysis by the scale-dependent Lyapunov exponent (SDLE).
Appendix A: Description of data.
Appendix B: Principal Component Analysis (PCA), Singular Value. Decomposition (SVD), and Karhunen-Loève (KL) expansion.
Appendix C: Complexity measures.
References.
Index.
Yinhe Cao is the CEO of BioSieve.
Wen-wen Tung is an Assistant Professor of the Department of Earth and Atmospheric Sciences at Purdue University, West Lafayette, Indiana.
Jing Hu is a Research Engineer of the Department of Electrical and Computer Engineering at the University of Florida.
