Fractional order control strategies for power electronic buck converters
Signal Processing - Fractional calculus applications in signals and systems
Energy separation in signal modulations with application to speechanalysis
IEEE Transactions on Signal Processing
Multicomponent AM–FM Representations: An Asymptotically Exact Approach
IEEE Transactions on Audio, Speech, and Language Processing
Automatica (Journal of IFAC)
Technical communique: A note on fractional-order derivatives of periodic functions
Automatica (Journal of IFAC)
Maximum number of frequencies in oscillations generated by fractional order LTI systems
IEEE Transactions on Signal Processing
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In this paper, undamped oscillations generated by fractional order systems are studied. At first, the trajectories of marginally stable fractional order systems with commensurate order are investigated and the differences with the integer order case are highlighted. Then, amplitude and frequency of oscillations in the steady state are analytically determined for these systems. It is shown that for a linear time invariant commensurate fractional order system, the maximum number of frequencies exists in the Fourier spectrum of the oscillations is half of its inner dimension, which is the same property as in the linear time invariant integer order systems. However, we show that this property is not necessarily exists for the incommensurate fractional order systems. Finally, the paper is closed by posing an open problem in this filed.