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:
- DNA sequence analysis
- EEG analysis
- Heart rate variability analysis
- Neural information processing
- Network traffic modeling
- Economic time series analysis
- 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.Content:
Chapter 1 Introduction (pages 1–14):
Chapter 2 Overview of Fractal and Chaos Theories (pages 15–24):
Chapter 3 Basics of Probability Theory and Stochastic Processes (pages 25–52):
Chapter 4 Fourier Analysis and Wavelet Multiresolution Analysis (pages 53–67):
Chapter 5 Basics of Fractal Geometry (pages 69–77):
Chapter 6 Self?Similar Stochastic Processes (pages 79–98):
Chapter 7 Stable Laws and Levy Motions (pages 99–113):
Chapter 8 Long Memory Processes and Structure?Function–Based Multifractal Analysis (pages 115–151):
Chapter 9 Multiplicative Multifractals (pages 153–180):
Chapter 10 Stage?Dependent Multiplicative Processes (pages 181–193):
Chapter 11 Models of Power?Law?Type Behavior (pages 195–211):
Chapter 12 Bifurcation Theory (pages 213–234):
Chapter 13 Chaotic Time Series Analysis (pages 235–259):
Chapter 14 Power?Law Sensitivity to Initial Conditions (PSIC)—An Interesting Connection Between Chaos Theory and Random Fractal Theory (pages 261–269):
Chapter 15 Multiscale Analysis by the Scale?Dependent Lyapunov Exponent (SDLE) (pages 271–305):