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 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.

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.