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:
* 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.
Autorentext
Jianbo Gao is an Assistant Professor of the Department of Electrical and Computer Engineering at the University of Florida.
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.
Klappentext
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:
-
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.
Zusammenfassung
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:
- 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.
Inhalt
Preface.
1. Introduction.
1.1 Examples of multiscale phenomena.
1.2 Examples of challenging problems to be pursued.
1.3 Outline of the book.
1.4 Bibliographic notes.
2. Overview of fractal and chaos theory.
2.1 Prelude to fractal geometry.
2.2 Prelude to chaos theory.
2.3 Further reading and bibliographic notes.
2.4 Warming up exercises.
3. Basics of probability theory and stochastic processes.
3.1 Basic elements of probability theory.
3.1.1 Probability system.
3.1.2 Random variables.
3.1.3 Expectation.
3.1.4 Characteristic function, moment generating function, Laplace.
transform, and probability generating function.
3.2 Commonly used distributions.
3.3 Stochastic processes.
3.3.1 Basic definitions.
3.3.2 Markov processes.
3.4 Special topic: How to find relevant information for a new field quickly?.
3.5 Bibliographic notes.
3.6 Exercises.
4. Fourier analysis and wavelet multiresolution analysis.
4.1 Fourier analysis.
4.1.1 Continuous-time signals.
4.1.2 Discrete-time signals.
4.1.3 Sampling theorem.
4.1.4 Discrete Fourier transform.
4.1.5 Fourier analysis of real data.
4.2 Wavelet multiresolution analysis.
4.3 Bibliographic notes.
4.4 Exercises.
5. Basics of fractal geometry.
5.1 The notion of dimension.
5.2 Geometrical fractals.
5.2.1 Cantor sets.
5.2.2 Von Koch curves.
5.3 Power-law and perception of self-similarity.
5.4 Bibliographical notes.
5.5 Exercises.
6. Self-similar stochastic processes.
6.1 General definition.
6.2 Brownian motion (Bm).
6.3 Fractional Brownian motion (fBm).
6.4 Dimensions of Bm and fBm processes.
6.5 Wavelet representation of fBm processes.
6.6 Synthesis of fBm processes.
6.7 Applications.
6.7.1 Network traffic modeling.
6.7.2 Modeling of rough surfaces.
6.8 Bibliographical notes.
6.9 Exercises.
7. Stable laws and Levy motions.
7.1 Stable distributions.
7.2 Summation of strictly stable random variables.
7.3 Tail probabilities and extreme events.
7.4 Generalized central limit theorem.
7.5 Levy motions.
7.6 Simulation of stable random variables.
7.7 Bibliographical notes.
7.8 Exercises.
8. Long memory processes and structure-function-based multifractal analysis.
8.1 Long memory: basic definitions.
8.2 Estimation of the Hurst parameter.
8.3 Random walk representation and structure function based multifractal analysis.
8.3.1 Random walk representation.
8.3.2 Structure function based multifractal analysis.
8.3.3 Understanding the Hurst parameter through multifractal analysis.
8.4 Other random-walk based scaling parameter estimation.
8.5 Other formulations of multifractal analysis.
8.6 The notion of finite scaling and consistency of estimators.
8.7 Correlation structure of ON/OFF intermittency and Levy motions.
8.7.1 …