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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.

Fractional Processes and Fractional-Order Signal Processing: Techniques and Applications

Part I: Overview of Fractional Processes and Fractional-order Signal Processing.- Introduction.- Overview of Fractional Processes and Fractional-order Signal Processing.- Part II: Fractional Processes.- Constant-order Fractional Processes.- Multifractional Processes.- Part III: Fractional-order Signal Processing.- Constant-order Fractional Signal Processing.- Variable-order Fractional Signal Processing.- Distributed-order Fractional Signal Processing.- Part IV: Applications of Fractional-order Signal Processing Techniques.- FARIMA with Stable Innovations Model of Great Salt Lake Elevation.- Analysis of ECN Using Fractional Signal Processing Techniques.- Optimal Fractional-order Damping Strategies.- Heavy-tailed Distribution and Local Long Memory in Molecular Motion.- Multifractional Property Analysis of Human Sleep EEG Signals.- Conclusions.- Appendices: Mittag-Leffler Functions; Application of Numerical Inverse Laplace Transform Algorithms in Fractional-order Signal Processing; Some Useful Webpages; MATLAB® Codes of Impulse-Response Invariant Discretization of Fractional-order Filters.