Fractional Processes and Fractional-Order Signal Processing

Beschreibung

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.
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.
Clear introduction to the need for and existing tools of inquiry into the world of fractional-order signal processing Emphasizes a computational approach with MATLAB® codes provided Practical real-world applications in diverse fields are presented as examples of the usefulness of fractional-order signal-processing techniques Includes supplementary material: sn.pub/extras

Autor*in

Hu Sheng

Themen in »Fractional Processes and Fractional-Order Signal Processing«

Fractional Fourier Transform Fractional-order Random Processes Fractional-order Signal Processing Long-range Dependence Nonstationary Stochastic Processes Stable Processes information and communication, circuits

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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)

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