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Fractional Processes and Fractional-Order Signal Processing: Techniques and Applications 2012 [Hardback]

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  • Formāts: Hardback, 295 pages, height x width: 235x155 mm, weight: 653 g, XXVI, 295 p., 1 Hardback
  • Sērija : Signals and Communication Technology
  • Izdošanas datums: 26-Oct-2011
  • Izdevniecība: Springer London Ltd
  • ISBN-10: 1447122321
  • ISBN-13: 9781447122326
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Fractional Processes and Fractional-Order Signal Processing: Techniques and Applications 2012Palielināt
  • Formāts: Hardback, 295 pages, height x width: 235x155 mm, weight: 653 g, XXVI, 295 p., 1 Hardback
  • Sērija : Signals and Communication Technology
  • Izdošanas datums: 26-Oct-2011
  • Izdevniecība: Springer London Ltd
  • ISBN-10: 1447122321
  • ISBN-13: 9781447122326
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781447122326.html
Keywords:
Fractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the 'fractional' perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing:   presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems;   introduces FOSP techniques and the fractional signals and fractional systems point of view;   details real-world-application examples of FOSP techniques to demonstrate their utility; and   provides important background material on Mittag-Leffler functions, the use of numerical inverse Laplace transform algorithms and supporting MATLAB® codes together with a helpful survey of relevant webpages. Readers will be able to use the techniques presented to re-examine their signals and signal-processing methods. This text offers an extended toolbox for complex signals from diverse fields in science and engineering. It will give academic researchers and practitioners a novel insight into the complex random signals characterized by fractional properties, and some powerful tools to analyze those signals.

This book describes complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations. Coverage includes simulation, fractional-order modeling and filtering fractional-order systems.

Recenzijas

From the reviews:

The book presents the theory and applications of an interesting domain in the area of signal science and technology: fractional processes and fractional order signal processing. The volume gives answers to several important questions related to fractional systems . A collection of very useful MATLAB codes is gives together with a useful list of Web addresses. Finally, we think that the present volume will soon become a reference book in the area of fractional signal processing and systems. (Dumitru Stanomir, Zentralblatt MATH, Vol. 1245, 2012)

Part I Overview of Fractional Processes and Fractional-Order Signal Processing Techniques
1 Introduction
3(28)
1.1 An Introduction to Fractional Processes and Analysis Methods
3(3)
1.2 Basis of Stochastic Processes
6(4)
1.2.1 Statistics of Stochastic Processes
6(1)
1.2.2 Properties of Stochastic Processes
7(2)
1.2.3 Gaussian Distribution and Gaussian Processes
9(1)
1.2.4 Stationary Processes
10(1)
1.3 Analysis of Random Signals
10(9)
1.3.1 Estimation of Properties for Stochastic Signals
10(2)
1.3.2 Simulation of Random Signals
12(1)
1.3.3 Signal Filtering
13(2)
1.3.4 Modeling Random Processes
15(1)
1.3.5 Transform Domain Analysis
16(3)
1.3.6 Other Analysis Methods
19(1)
1.4 Research Motivation
19(4)
1.4.1 Heavy Tailed Distributions
19(1)
1.4.2 Long Range Dependence
20(2)
1.4.3 Local Memory
22(1)
1.5 Basics of Fractional-Order Signal Processing
23(5)
1.5.1 Fractional Calculus
23(2)
1.5.2 α-Stable Distribution
25(1)
1.5.3 Fractional Fourier Transform
26(2)
1.6 Brief Summary of Contributions of the Monograph
28(1)
1.7 Structure of the Monograph
28(3)
2 An Overview of Fractional Processes and Fractional-Order Signal Processing Techniques
31(18)
2.1 Fractional Processes
31(8)
2.1.1 Fractional Processes and Fractional-Order Systems
32(3)
2.1.2 Stable Processes
35(1)
2.1.3 Fractional Brownian Motion
36(1)
2.1.4 Fractional Gaussian Noise
37(1)
2.1.5 Fractional Stable Motion
37(1)
2.1.6 Fractional Stable Noise
38(1)
2.1.7 Multifractional Brownian Motion
38(1)
2.1.8 Multifractional Gaussian Noise
38(1)
2.1.9 Multifractional Stable Motion
39(1)
2.1.10 Multifractional Stable Noise
39(1)
2.2 Fractional-Order Signal Processing Techniques
39(7)
2.2.1 Simulation of Fractional Random Processes
39(1)
2.2.2 Fractional Filter
40(1)
2.2.3 Fractional-Order Systems Modeling
41(1)
2.2.4 Realization of Fractional Systems
41(2)
2.2.5 Other Fractional Tools
43(3)
2.3
Chapter Summary
46(3)
Part II Fractional Processes
3 Constant-Order Fractional Processes
49(28)
3.1 Introduction of Constant-Order Fractional Processes
49(7)
3.1.1 Long-Range Dependent Processes
49(2)
3.1.2 Fractional Brownian Motion and Fractional Gaussian Noise
51(2)
3.1.3 Linear Fractional Stable Motion and Fractional Stable Noise
53(3)
3.2 Hurst Estimators: A Brief Summary
56(4)
3.2.1 R/S Method [ 194]
56(1)
3.2.2 Aggregated Variance Method [ 22]
56(1)
3.2.3 Absolute Value Method [ 297]
57(1)
3.2.4 Variance of Residuals Method [ 298]
57(1)
3.2.5 Periodogram Method and the Modified Periodogram Method [ 97, 113]
57(1)
3.2.6 Whittle Estimator [ 298]
58(1)
3.2.7 Diffusion Entropy Method [ 105]
58(1)
3.2.8 Kettani and Gubner's Method [ 138]
59(1)
3.2.9 Abry and Veitch's Method [ 1]
59(1)
3.2.10 Koutsoyiannis' Method [ 153]
59(1)
3.2.11 Higuchi's Method [ 116]
60(1)
3.3 Robustness of Hurst Estimators
60(16)
3.3.1 Test Signal Generation and Estimation Procedures
61(1)
3.3.2 Comparative Results and Robustness Assessment
62(12)
3.3.3 Quantitative Robustness Comparison and Guideline for Selection Estimator
74(2)
3.4
Chapter Summary
76(1)
4 Multifractional Processes
77(18)
4.1 Multifractional Processes
78(1)
4.1.1 Multifractional Brownian Motion and Multifractional Gaussian Noise
78(1)
4.1.2 Linear Multifractional Stable Motion and Multifractional Stable Noise
79(1)
4.2 Tracking Performance and Robustness of Local Holder Exponent Estimator
79(13)
4.2.1 Test Signal Generation and Estimation Procedures
80(2)
4.2.2 Estimation Results
82(9)
4.2.3 Guideline for Estimator Selection
91(1)
4.3
Chapter Summary
92(3)
Part III Fractional-Order Signal Processing
5 Constant-Order Fractional Signal Processing
95(54)
5.1 Fractional-Order Differentiator/Integrator and Fractional Order Filters
95(34)
5.1.1 Continuous-Time Implementations of Fractional-Order Operators
96(5)
5.1.2 Discrete-Time Implementation of Fractional-Order Operators
101(19)
5.1.3 Frequency Response Fitting of Fractional-Order Filters
120(3)
5.1.4 Transfer Function Approximations to Complicated Fractional-Order Filters
123(2)
5.1.5 Sub-optimal Approximation of Fractional-Order Transfer Functions
125(4)
5.2 Synthesis of Constant-Order Fractional Processes
129(2)
5.2.1 Synthesis of Fractional Gaussian Noise
129(2)
5.2.2 Synthesis of Fractional Stable Noise
131(1)
5.3 Constant-Order Fractional System Modeling
131(5)
5.3.1 Fractional Autoregressive Integrated Moving Average Model
132(1)
5.3.2 Gegenbauer Autoregressive Moving Average Model
133(1)
5.3.3 Fractional Autoregressive Conditional Heteroscedastieity Model
134(1)
5.3.4 Fractional Autoregressive Integrated Moving Average with Stable Innovations Model
134(2)
5.4 A Fractional Second-Order Filter
136(9)
5.4.1 Derivation of the Analytical Impulse Response of (s2+as+b)γ
136(4)
5.4.2 Impulse Response Invariant Discretization of (s2+as+b)γ
140(5)
5.5 Analogue Realization of Constant-Order Fractional Systems
145(3)
5.5.1 Introduction of Fractional-Order Component
145(1)
5.5.2 Analogue Realization of Fractional-Order Integrator and Differentiator
146(2)
5.6
Chapter Summary
148(1)
6 Variable-Order Fractional Signal Processing
149(12)
6.1 Synthesis of Multifractional Processes
149(3)
6.1.1 Synthesis of mGn
149(2)
6.1.2 Examples of the Synthesized mGns
151(1)
6.2 Variable-Order Fractional System Modeling
152(2)
6.2.1 Locally Stationary Long Memory FARIMA(p, dt, q) Model
152(2)
6.2.2 Locally Stationary Long Memory FARIMA(p, dr, q) with Stable Innovations Model
154(1)
6.2.3 Variable Parameter FIGARCH Model
154(1)
6.3 Analogue Realization of Variable-Order Fractional Systems
154(5)
6.3.1 Physical Experimental Study of Temperature-Dependent Variable-Order Fractional Integrator and Differentiator
154(4)
6.3.2 Application Examples of Analogue Variable-Order Fractional Systems
158(1)
6.4
Chapter Summary
159(2)
7 Distributed-Order Fractional Signal Processing
161(18)
7.1 Distributed-Order Integrator/Differentiator
162(5)
7.1.1 Impulse Response of the Distributed-Order Integrator/Differentiator
163(2)
7.1.2 Impulse Response Invariant Discretization of DOUDOD
165(2)
7.2 Distributed-Order Low-Pass Filter
167(4)
7.2.1 Impulse Response of the Distributed-Order Low-Pass Filter
168(1)
7.2.2 Impulse Response Invariant Discretization of DO-LPF
169(2)
7.3 Distributed Parameter Low-Pass Filter
171(4)
7.3.1 Derivation of the Analytical Impulse Response of the Fractional-Order Distributed Parameter Low-Pass Filter
172(2)
7.3.2 Impulse Response Invariant Discretization of FO-DP-LPF
174(1)
7.4
Chapter Summary
175(4)
Part IV Applications of Fractional-Order Signal Processing Techniques
8 Fractional Autoregressive Integrated Moving Average with Stable Innovations Model of Great Salt Lake Elevation Time Series
179(10)
8.1 Introduction
179(1)
8.2 Great Salt Lake Elevation Data Analysis
180(4)
8.3 FARIMA and FIGARCH Models of Great Salt Lake Elevation Time Series
184(1)
8.4 FARIMA with Stable Innovations Model of Great Salt Lake Elevation Time Series
185(2)
8.5
Chapter Summary
187(2)
9 Analysis of Biocorrosion Electrochemical Noise Using Fractional Order Signal Processing Techniques
189(14)
9.1 Introduction
189(1)
9.2 Experimental Approach and Data Acquisition
190(1)
9.3 Conventional Analysis Techniques
190(6)
9.3.1 Conventional Time Domain Analysis of ECN Signals
190(2)
9.3.2 Conventional Frequency Domain Analysis
192(4)
9.4 Fractional-Orders Signal Processing Techniques
196(5)
9.4.1 Fractional Fourier Transform Technique
196(1)
9.4.2 Fractional Power Spectrum Density
197(2)
9.4.3 Self-similarity Analysis
199(2)
9.4.4 Local Self-similarity Analysis
201(1)
9.5
Chapter Summary
201(2)
10 Optimal Fractional-Order Damping Strategies
203(14)
10.1 Introduction
203(1)
10.2 Distributed-Order Fractional Mass-Spring Viscoelastic Damper System
204(2)
10.3 Frequency-Domain Method Based Optimal Fractional-Order Damping Systems
206(3)
10.4 Time-Domain Method Based Optimal Fractional-Order Damping Systems
209(5)
10.5
Chapter Summary
214(3)
11 Heavy-Tailed Distribution and Local Memory in Time Series of Molecular Motion on the Cell Membrane
217(16)
11.1 Introduction
217(1)
11.2 Heavy-Tailed Distribution
218(1)
11.3 Time Series of Molecular Motion
219(2)
11.4 Infinite Second-Order and Heavy-Tailed Distribution in Jump Time Series
221(2)
11.5 Long Memory and Local Memory in Jump Time Series
223(3)
11.6
Chapter Summary
226(7)
12 Non-linear Transform Based Robust Adaptive Latency Change Estimation of Evoked Potentials
233(10)
12.1 Introduction
233(1)
12.2 DLMS and DLMP Algorithms
234(2)
12.2.1 Signal and Noise Model
234(1)
12.2.2 DLMS and Its Degradation
234(1)
12.2.3 DLMP and Its Improvement
235(1)
12.3 NLST Algorithm
236(3)
12.3.1 NLST Algorithm
236(1)
12.3.2 Robustness Analysis of the NLST
236(3)
12.4 Simulation Results and Discussion
239(3)
12.5
Chapter Summary
242(1)
13 Multifractional Property Analysis of Human Sleep Electroencephalogram Signals
243(8)
13.1 Introduction
243(1)
13.2 Data Description and Methods
244(1)
13.2.1 Data Description
244(1)
13.2.2 Methods
245(1)
13.3 Fractional Property of Sleep EEG Signals
245(3)
13.4 Multifractional Property of Sleep EEG Signals
248(2)
13.5
Chapter Summary
250(1)
14 Conclusions
251(2)
Appendix A Mittag-Leffler Function 253(4)
Appendix B Application of Numerical Inverse Laplace Transform Algorithms in Fractional-Order Signal Processing 257(10)
B.1 Introduction
257(1)
B.2 Numerical Inverse Laplace Transform Algorithms
258(1)
B.3 Some Application Examples of Numerical Inverse Laplace Transform Algorithms in Fractional Order Signal Processing
259(7)
B.3.1 Example A
259(1)
B.3.2 Example B
260(1)
B.3.3 Example C
261(2)
B.3.4 Example D
263(1)
B.3.5 Example E
263(3)
B.4 Conclusion
266(1)
Appendix C Some Useful Webpages 267(2)
C.1 Useful Homepages
267(1)
C.2 Useful Codes
267(2)
Appendix D MATLAB Codes of Impulse Response Invariant Discretization of Fractional-Order Filters 269(10)
D.1 Impulse Response Invariant Discretization of Distributed-Order Integrator
269(3)
D.2 Impulse Response Invariant Discretization of Fractional Second-Order Filter
272(3)
D.3 Impulse Response Invariant Discretization of Distributed-Order Low-Pass Filter
275(4)
References 279(14)
Index 293
Doctor YangQuan Chen has authored over 200 academic papers plus numerous technical reports. He co-authored two textbooks: "System Simulation Techniques with MATLAB®/Simulink" (with Dingyu Xue . Tsinghua University Press, April 2002, ISBN 7-302-05341-3/TP3137, in Chinese) and "Solving Advanced Applied Mathematical Problems Using Matlab" (with Dingyu Xue. Tsinghua University Press. August 2004. 419 pages in Chinese, ISBN 7-302-09311-3/O.392); and six research monographs: "Plastic Belt for Projectiles" (with Y. Shi. Shaanxi Science and Technology Press, Jan. 1995, ISBN 7-5369-2277-9/TJ.1, in Chinese), "Iterative Learning Control " (with C. Wen . Lecture Notes in Control and Information Sciences, Springer-Verlag, Nov. 1999, ISBN: 978-1-85233-190-0), Iterative Learning Control (with Hyo-Sung Ahn and Kevin L. Moore. Springer, July 2007, ISBN: 978-1-84628-846-3), Optimal Observation for Cyber-physical Systems(with Zhen Song, Chellury Sastry and Nazif Tas. Springer, July 2009, ISBN: 978-1-84882-655-7), Fractional-order Systems and Controls (with Concepción A. Monje, Blas M. Vinagre, Dingyu Xue and Vicente Feliu, ISBN: 978-1-84996-334-3), and Optimal Mobile Sensing and Actuation Strategies in Cyber-physical Systems (with Christophe Tricaud). His current research interests include autonomous navigation and intelligent control of a team of unmanned ground vehicles, machine vision for control and automation, distributed control systems (MAS-net: mobile actuator-sensor networks), fractional-order control, interval computation, and iterative/repetitive/adaptive learning control. Currently, he serves as an Associate Editor for IEEE Control Systems Society, Conference Editorial Board (CSSCEB ). He was also an Associate Editor of ISA Review Board for AACC 's American Control Conference ( ACC2005 ). He has been the Co-Organizer and Instructor of the Tutorial Workshops on Fractional-order Calculus in Control and Robotics at IEEE 2002 Conference onDecision and Control (CDC02), and Applied Fractional Calculus in Controls and Signal Processing at CDC10 and a founding member of the ASME subcommittee on Fractional Dynamics.