Fractional-order inverting and non-inverting filters based on CFOA

2016Madian A.H.Radwan A.G.Said L.A.Soliman A.M.

This paper introduces a study to generalize the design of a continuous time filters into the fractional order domain. The study involves inverting and non-inverting filters based on CFOA where three responses are extracted which are high-pass, band-pass and low-pass responses. The proposed study introduces the generalized formulas for the transfer function of each response with different fractional orders. The fractional-order filters enhance the design flexibility and controllability due to the extra degree of freedom provided by the fractional order parameters. The general fundamentals of these filters are presented by calculating the cutoff frequency equation. Different numerical solutions for the generalized fractional order filters are introduced. Stability discussion is presented for different fractional order cases. Spice simulations results are introduced to validate the theoretical findings. © 2016 IEEE.

Fractional-order oscillator based on single CCII

2016Madian A.H.Radwan A.G.Said L.A.Soliman A.M.

This paper presents a generalization of well-known phase shift oscillator based on single CCII into the fractional order domain. The general state matrix, characteristic equation and design equations are presented. The general oscillation frequency, condition and the phase difference between the oscillatory outputs are introduced in terms of the fractional order parameters. These parameters add extra degrees of freedom which in turn increase the design flexibility and controllability. Numerical discussion of five special cases is investigated including the integer case. Spice simulations and experimental results are introduced to validate the theoretical findings with stability discussion. © 2016 IEEE.

Charging and discharging RC? circuit under Riemann-Liouville and Caputo fractional derivatives

2016Abdelaty A.M.Ahmed W.A.Faied M.Radwan A.G.

In this paper, the effect of non-zero initial condition on the time domain responses of fractional-order systems using Caputo and Riemann-Liouville (RL) fractional definitions are discussed. Analytical formulas were derived for the step and square wave responses of fractional-order RC? circuit under RL and Caputo operators for non-zero initial condition. Moreover, a simulation scheme for fractional state-space systems with non-zero initial condition is introduced. © 2016 IEEE.

Low pass filter design based on fractional power chebyshev polynomial

2016Abdelaty A.M.Ahmed W.A.Radwan A.G.Soltan A.

This paper introduces the design procedure for the low pass filter based on Chebyschev polynomials of fractional power of any order. The filter order is considered in intervals of width two. Only the first two intervals are considered along with their pole locus produced by varying the filter order and the magnitude response. A general formula for constructing the filter from its s-plane poles is suggested. Numerical analysis and circuit simulations using MATLAB and Advanced Design System (ADS) based on the proposed design procedure are presented. Good matching between the circuit simulation and the numerical analysis is obtained which proves the reliability of the proposed design procedure. © 2015 IEEE.

Design of a generalized bidirectional tent map suitable for encryption applications

2016Fahmy H.A.H.Radwan A.G.Sayed W.S.

The discrete tent map is one of the most famous discrete chaotic maps that has widely-spread applications. This paper investigates a set of four generalized tent maps where the conventional map is a special case. The proposed maps have extra degrees of freedom which provide different chaotic characteristics and increase the design flexibility required for many applications. Mathematical analyses for generalized positive and mostly positive tent maps include: bifurcation diagrams relative to all parameters, effective range of parameters, bifurcation points. The maximum Lyapunov exponent (MLE) is also calculated to indicate chaotic behavior. Various scales of the bifurcation diagram are discussed for each generalized map as well as system responses versus the added parameters. © 2015 IEEE.