Fractional Processes and Fractional-Order Signal Processing [electronic resource] : Techniques and Applications /
Sheng, Hu.author.
Chen, YangQuan.author.
Qiu, TianShuang.author.
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.
Description based upon print version of record.
Includes bibliographical references and index.
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.
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.
Signal processing.
Image processing.
Speech processing systems.
Optical data processing.
Information theory.
Signal, Image and Speech Processing.
Image Processing and Computer Vision.
Information and Communication, Circuits.
Signals and Communication Technology