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
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.
Hermite polynomials in the fractional order domain suitable for special filters design
This paper introduces the design procedure for the low pass filter based on Chebyschev polynomials of fractional power of any order
Fractional order Chebyshev-like low-pass filters based on integer order poles
Chebyshev filter is one of the most commonly used prototype filters that approximate the ideal magnitude response. In this paper, a simple and fast approach to create fractional order Chebyshev-like filter using its integer order poles is discussed. The transfer functions for the fractional filters are developed using the integer order poles from the traditional filter. This approach makes this work the first to generate fractional order transfer functions knowing their poles. The magnitude, phase, step responses, and group delay are simulated for different fractional orders showing their Chebyshev-like characteristics while achieving a fractional order slope. Circuit simulations using Advanced Design Systems of active and passive realizations of the proposed filters are also included and compared with Matlab numerical simulations proving the reliability of the design procedure. Experimental results of a two-stage active realization show good accordance with ADS and Matlab results. © 2019 Elsevier Ltd
On the Analysis and Design of Fractional-Order Chebyshev Complex Filter
This paper introduces the concept of fractional-order complex Chebyshev filter