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(R) 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.
