Synthesis of multifractional Gaussian noises based on variable-order fractional operators

Signal Processing

Volumn 91, Issue 7, 2011, Pages 1645-1650

  Sheng, Hu ^a,b   Sun, Hongguang ^b,c   Chen, Yangquan ^b   Qiu, Tianshuang ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b Utah State University   (United States)

^c HOHAI UNIVERSITY   (China)

Author keywords

Fractional Gaussian noise (fGn); Fractional order signal processing (FOSP); Multifractional stable noise; Multifractional Brownian motion (mBm); Multifractional Gaussian noise (mGn); Variable order fractional operator

Indexed keywords

FRACTIONAL GAUSSIAN NOISE (FGN); FRACTIONAL-ORDER SIGNAL PROCESSING (FOSP); MULTIFRACTIONAL BROWNIAN MOTION (MBM); MULTIFRACTIONAL GAUSSIAN NOISE (MGN); VARIABLE-ORDER FRACTIONAL OPERATOR;

BROWNIAN MOVEMENT; GAUSSIAN NOISE (ELECTRONIC); SIGNAL PROCESSING; STABILITY CRITERIA; TORQUE CONTROL;

GAUSSIAN DISTRIBUTION;

EID: 79952043566     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2011.01.010     Document Type: Article

References (43)

1. M.E. Crovella, and A. Bestavros Self-similarity in world wide web traffic evidence and possible causes IEEE/ACM Transactions on Networking 5 6 1997 835 846 (Pubitemid 127768491)
2. H.E. Hurst Long-term storage capacity of reservoirs Transactions of the American Society of Civil Engineers 116 3 1951 770 799
3. G. Samorodnitsky, and M.S. Taqqu Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance first ed. 1994 Chapman and Hall
4. K. Burnecki, and A. Weron Levy stable processes. From stationary to self-similar dynamics and back. An application to finance Acta Physica Polonica B 35 4 2004 1343 1358
5. M. Li, Fractal time seriesa tutorial review, Mathematical Problems in Engineering 2010, doi: 10.1155/2010/157264.
6. D.O. Cajueiro, and B.M. Tabak Time-varying long-range dependence in US interest rates Chaos, Solitons and Fractals 34 2 2007 360 367 (Pubitemid 46562568)
7. K.J. Falconer The local structure of random processes Journal of the London Mathematical Society 67 3 2003 657 672 (Pubitemid 36742711)
8. B. Pesquet-Popescu, and J.-C. Pesquet Synthesis of bidimensional α stable models with long-range dependence Signal Processing 82 12 2002 1927 1940 (Pubitemid 35214249)
9. H. Sheng, and Y.Q. Chen FARIMA with stable innovations model of Great Salt Lake elevation time series Signal Processing 91 3 2011 553 561
10. A. Loverro, Fractional calculus: history, definitions and applications for the engineer, Report, Department of Aerospace and Mechanical Engineering, Notre Dame, IN 46556, USA, May 2004.
11. Y.Q. Chen, R. Sun, A. Zhou, and N. Zaveri Fractional order signal processing of electrochemical noises Journal of Vibration and Control 14 910 2008 1443 1456
12. T.T. Hartley, and C.F. Lorenzo Fractional-order system identification based on continuous order-distributions Signal Processing 83 11 2003 2287 2300
13. R.L. Wolpert, and M.S. Taqqu Fractional OrnsteinUhlenbeck Lvy processes and the telecom process: upstairs and downstairs Signal Processing 85 8 2005 1523 1545 (Pubitemid 40762451)
14. S.G. Samko Fractional integration and differentiation of variable order Analysis Mathematica 21 3 1995 213 236
15. B. Ross, and S.G. Samko Fractional integration operator of variable order in the Hlder spaces Hλ (x ) International Journal of Mathematics and Mathematical Sciences 18 4 1995 777 788
16. C.F. Lorenzo, and T.T. Hartley Variable order and distributed order fractional operators Nonlinear Dynamics 29 1/4 2002 57 98 (Pubitemid 34945393)
17. Y. Li, H. Sheng, Y.Q. Chen, On distributed order integrator/ differentiator, Signal Processing, 2010, this issue, doi: 10.1016/j.sigpro.2010. 10.005
18. M.D. Ortigueira Introduction to fractional linear systems. Part 1. continuous-timecase Vision, Image and Signal Processing, IEE Proceedings 147 1 2000 62 70 (Pubitemid 30589669)
19. Y.Q. Chen, R. Sun, and A. Zhou An improved Hurst parameter estimator based on fractional Fourier transform Telecommunication Systems 43 34 2010 197 206
20. B.B. Mandelbrot, and J.W.V. Ness Fractional Brownian motions, fractional noises and applications SLAM Review 10 4 1968 422 437
21. J. Beran Statistics for Long-Memory Processes first ed. 1994 CRC Press
22. M.D. Ortigueira, and A.G. Batista On the relation between the fractional Brownian motion and the fractional derivatives Physics Letters A 372 7 2008 958 968
23. R.F. Peltier, J.L. Vehel, Multifractional Brownian motion: definition and preliminary results, Technical Report, Institut National De Recherche En Informatique Et En Automatique, 1995.
24. S. Cohen, and R. Marty Invariance principle, multifractional Gaussian processes and long-range dependence Annales de l'Institut Henri Poincar'eProbabilit'es et Statistiques 44 3 2008 475 489
25. S.V. Muniandy, and S.C. Lim Modeling of locally self-similar processes using multifractional Brownian motion of RiemannLiouville type Physical Review E 63 4 2001
26. L.E.S. Ramirez, C.F.M. Coimbra, On the selection and meaning of variable order operators for dynamic modeling, International Journal of Differential Equations, doi: 10.1155/2010/846107.
27. R. Navarro Jr., R. Tamangan, N. Guba-Natan, E. Ramos, and A.D. Guzman The identification of long memory process in the Asean-4 stock markets by fractional and multifractional Brownian motion The Philippine Statistician 55 12 2006 65 83
28. A.N. Kolmogorov Wienersche spiralen und einige, andere interessante kurven in hilbertschen raum Computes Rendus (Doklady) Academic Sciences USSR (NS) 26 1940 115 118
29. M.S. Taqqu, and V. Teverovsky Robustness of Whittle type estimators for time series with long-range dependence Stochastic Models 13 4 1997 723 757 (Pubitemid 127763071)
30. S.C. Lim Fractional Brownian motion and multifractional Brownian motion of RiemannLiouville type Journal of Physics A: Mathematical and General 34 2001 1301 1310
31. I. Podlubny Fractional Differential Equations first ed. 1999 Academic Press
32. D. Ingman, and J. Suzdalnitsky Application of differential operator with servo-order function in model of viscoelastic deformation process Journal of Engineering Mechanics 131 7 2005 763 767 (Pubitemid 41065463)
33. D. Ingman, J. Suzdalnitsky, and M. Zeifman Constitutive dynamic-order model for nonlinear contact phenomena Journal of Applied Mechanics 67 2 2000 383 390
34. C.F.M. Coimbra Mechanics with variable-order differential operators Annalen der Physik 12 1112 2003 692 703
35. H. Sun, W. Chen, and Y.Q. Chen Variable-order fractional differential operators in anomalous diffusion modeling Physica A 338 21 2009 4586 4592
36. C.M. Soon, C.F.M. Coimbra, and M.H. Kobayashi Variable order differential equations and diffusion processes with changing modes Annalen der Physik 517 6 2005 378 389
37. C.C. Tseng Design of variable and adaptive fractional order FIR differentiators Signal Processing 86 10 2005 2554 2566
38. Z. Santouh, A. Charef, and M. Assabaa Approximation of multiple fractional order systems Ariser 3 4 2007 155 161
39. H. Sun, W. Chen, H. Sheng, and Y. Chen On mean square displacement behaviors of anomalous diffusions with variable and random orders Physics Letters A 374 7 2010 906 910
40. J.A. Barnes, and D.W. Allan A statistical model of flicker noise Proceedings of the IEEE 54 2 1996 176 178
41. H. Sun, Predictor-corrector method for variable-order, random-order fractional relaxation equation, Matlab Central-File Exchange, 〈 http://www.mathworks.com/matlabcentral/fileexchange/26407 〉, 2010.
42. B.P. Popescu, and J.C. Pesquet Synthesis of bidimensional alpha-stable models with long-range dependence Signal Processing 82 12 2002 1927 1940
43. D. Koutsoyiannis Climate change, the Hurst phenomenon, and hydrological statistics Hydrological Sciences Journal 48 1 2003 3 24 (Pubitemid 36242577)