LEADER 05383nam 2200649 a 450 001 9910143568303321 005 20170815122431.0 010 $a1-280-97446-X 010 $a9786610974467 010 $a0-470-19165-1 010 $a0-470-19164-3 035 $a(CKB)1000000000355519 035 $a(EBL)315184 035 $a(OCoLC)476106267 035 $a(SSID)ssj0000303779 035 $a(PQKBManifestationID)11227126 035 $a(PQKBTitleCode)TC0000303779 035 $a(PQKBWorkID)10275723 035 $a(PQKB)11637567 035 $a(MiAaPQ)EBC315184 035 $a(EXLCZ)991000000000355519 100 $a20070504d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aMultiscale analysis of complex time series$b[electronic resource] $eintegration of chaos and random fractal theory, and beyond /$fJianbo Gao ... [et al.] 210 $aHoboken, N.J. $cWiley-Interscience$dc2007 215 $a1 online resource (368 p.) 300 $aDescription based upon print version of record. 311 $a0-471-65470-1 320 $aIncludes bibliographical references (p. 319-346) and index. 327 $aMultiscale Analysis of Complex Time Series; CONTENTS; 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 theories; 2.1 Prelude to fractal geometry; 2.2 Prelude to chaos theory; 2.3 Bibliographic notes; 2.4 Warmup 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 327 $a3.1.4 Characteristic function, moment generating function, Laplace transform, and probability generating function3.2 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 (CT) signals; 4.1.2 Discrete-time (DT) signals; 4.1.3 Sampling theorem; 4.1.4 Discrete Fourier transform; 4.1.5 Fourier analysis of real data 327 $a4.2 Wavelet multiresolution analysis4.3 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 Bibliographic 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 327 $a6.7.2 Modeling of rough surfaces6.8 Bibliographic 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 Bibliographic 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 327 $a8.3.1 Random walk representation8.3.2 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 H estimators; 8.7 Correlation structure of ON/OFF intermittency and Levy motions; 8.7.1 Correlation structure of ON/OFF intermittency; 8.7.2 Correlation structure of Levy motions; 8.8 Dimension reduction of fractal processes using principal component analysis; 8.9 Broad applications 327 $a8.9.1 Detection of low observable targets within sea clutter 330 $aThe 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 c 606 $aTime-series analysis 606 $aChaotic behavior in systems 606 $aFractals 608 $aElectronic books. 615 0$aTime-series analysis. 615 0$aChaotic behavior in systems. 615 0$aFractals. 676 $a519.5/5 676 $a621.3822 701 $aGao$b Jianbo$f1966-$0984002 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910143568303321 996 $aMultiscale analysis of complex time series$92246815 997 $aUNINA