Journal ArticleDOI
First-order filters generalized to the fractional domain
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This work shows that low-pass, high- pass, band-pass and all-pass filters can be realized with circuits incorporating a single fractance device and derives expressions for the pole frequencies, the quality factor, the right-phase frequencies, and the half-power frequencies.Abstract:
Traditional continuous-time filters are of integer order. However, using fractional calculus, filters may also be represented by the more general fractional-order differential equations in which case integer-order filters are only a tight subset of fractional-order filters. In this work, we show that low-pass, high-pass, band-pass, and all-pass filters can be realized with circuits incorporating a single fractance device. We derive expressions for the pole frequencies, the quality factor, the right-phase frequencies, and the half-power frequencies. Examples of fractional passive filters supported by numerical and PSpice simulations are given.read more
Citations
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Journal ArticleDOI
Fractional-order circuits and systems: An emerging interdisciplinary research area
TL;DR: A recent article published in this magazine has labeled fractional-order continuous-time systems as the "21st century systems" and highlighted specific problems which need to be addressed particularly by electrical engineers.
Journal ArticleDOI
Studies on fractional order differentiators and integrators: A survey
TL;DR: Fractional order differentiators and integrators of order 12 and 14 are designed and implemented in real time using TMS320C6713 DSP processor and tested using National instruments education laboratory virtual instrumentation system (NIELVIS).
Journal ArticleDOI
On the stability of linear systems with fractional-order elements
TL;DR: In this paper, the stability of linear integer-order circuits with one fractional element, two fractional elements of the same order or two fractions of different order is studied, and a general procedure for studying the system with many fractional components is also given.
Journal ArticleDOI
Fractional-Order Sinusoidal Oscillators: Design Procedure and Practical Examples
TL;DR: The Barhkausen condition for a linear noninteger-order (fractional-order) dynamical system to oscillate is derived and the oscillation condition and oscillation frequency of some famous integer-order sinusoidal oscillators can be obtained as special cases from general equations governing their fractional- order counterparts.
Journal ArticleDOI
On the generalization of second-order filters to the fractional-order domain
TL;DR: This work considers here the case where a filter is constructed using two fractional-order capacitors both of the same order α, and shows for the first time experimental results using the fractional capacitive probe described in Ref. 1.
References
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Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Book
Fractional Integrals and Derivatives: Theory and Applications
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
Proceedings Article
Stability results for fractional differential equations with applications to control processing
TL;DR: In this article, stability results for finite-dimensional linear fractional differential systems in state-space form are given for both internal and external stability, and the main qualitative result is that stabilities are guaranteed iff the roots of some polynomial lie outside the closed angular sector.
Journal Article
Basic Characteristics of a Fractance Device
Journal ArticleDOI
Realization of a Constant Phase Element and Its Performance Study in a Differentiator Circuit
TL;DR: A fractional-order differentiator circuit has been constructed using the CPE, and its performance has been compared with the simulated results.