An Overview of Fractional Processes and Fractional-Order Signal Processing Techniques

[1]  Scott L. Miller,et al.  Probability and Random Processes : With Applications to Signal Processing and Communications , 2012 .

[2]  V. Schmidt,et al.  Dielectric Properties of Lithium Hydrazinium Sulfate. , 1971 .

[3]  C. L. Nikias,et al.  Signal processing with alpha-stable distributions and applications , 1995 .

[4]  R. Peltier,et al.  Multifractional Brownian Motion : Definition and Preliminary Results , 1995 .

[5]  K. Moore,et al.  Discretization schemes for fractional-order differentiators and integrators , 2002 .

[6]  Z. Huang,et al.  On fractional stable processes and sheets: White noise approach , 2007 .

[7]  Y. Chen,et al.  Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives—an Expository Review , 2004 .

[8]  D. W. Allan,et al.  A statistical model of flicker noise , 1966 .

[9]  Carl F. Lorenzo,et al.  Variable Order and Distributed Order Fractional Operators , 2002 .

[10]  J. McCulloch,et al.  Simple consistent estimators of stable distribution parameters , 1986 .

[11]  Thierry Blu,et al.  Fractional Splines and Wavelets , 2000, SIAM Rev..

[12]  I. Podlubny.  Fractional differential equations , 1998 .

[13]  Alain Oustaloup,et al.  Frequency-band complex noninteger differentiator: characterization and synthesis , 2000 .

[14]  Manuel Duarte Ortigueira.  A new symmetric fractional B-spline , 2003, Signal Process..

[15]  Manuel Duarte Ortigueira,et al.  Introduction to fractional linear systems. Part 2. Discrete-time case , 2000 .

[16]  Chrysostomos L. Nikias,et al.  Joint estimation of time delay and frequency delay in impulsive noise using fractional lower order statistics , 1996, IEEE Trans. Signal Process..

[17]  Thierry Blu,et al.  The fractional spline wavelet transform: definition end implementation , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[18]  J. Geweke,et al.  THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS , 1983 .

[19]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[20]  Yangquan Chen,et al.  A new IIR-type digital fractional order differentiator , 2003, Signal Process..

[21]  John A. Gubner,et al.  Probability and Random Processes for Electrical and Computer Engineers , 2006 .

[22]  Manuel Duarte Ortigueira,et al.  Introduction to fractional linear systems. Part 1. Continuous-time case , 2000 .

[23]  E. Fama,et al.  Parameter Estimates for Symmetric Stable Distributions , 1971 .

[24]  Demetris Koutsoyiannis,et al.  Climate change, the Hurst phenomenon, and hydrological statistics , 2003 .

[25]  Yangquan Chen,et al.  An improved Hurst parameter estimator based on fractional Fourier transform , 2010, Telecommun. Syst..

[26]  D Mendlovic,et al.  Fractional Hilbert transform. , 1996, Optics letters.

[27]  W. Willinger,et al.  ESTIMATORS FOR LONG-RANGE DEPENDENCE: AN EMPIRICAL STUDY , 1995 .

[28]  Richard A. Davis,et al.  Time Series: Theory and Methods (2Nd Edn) , 1993 .

[29]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[30]  Ming Li.  Fractal Time Series—A Tutorial Review , 2010 .

[31]  S. C. Lim,et al.  Fractional Brownian motion and multifractional Brownian motion of Riemann-Liouville type , 2001 .

[32]  Monson H. Hayes,et al.  Statistical Digital Signal Processing and Modeling , 1996 .

[33]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[34]  G. Bohannan.  Analog Fractional Order Controller in Temperature and Motor Control Applications , 2008 .

[35]  Hongguang Sun,et al.  Synthesis of multifractional Gaussian noises based on variable-order fractional operators , 2011, Signal Process..

[36]  Discrete-time Case , 2013 .

[37]  M. Taqqu,et al.  Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance , 1995 .

[38]  C. Lubich.  Discretized fractional calculus , 1986 .

[39]  Mohamed Boutahar,et al.  A Simple Fractionally Integrated Model with a Time-varying Long Memory Parameter dt , 2008 .

[40]  H. E. Hurst,et al.  Long-Term Storage Capacity of Reservoirs , 1951 .

[41]  J. Zabczyk,et al.  Regularity of Ornstein–Uhlenbeck Processes Driven by a Lévy White Noise , 2008, 0901.0028.