Comparison of Different Implementation Methods of Fractional-Order Derivative/Integral

Implementing a fractional-order operator requires many resources to acquire an accurate response compared to the theoretical response. In this paper, three implementation methods of digital fractional-order operators are exploited. The three implementation methods are based on FIR, IIR, and lattice wave digital filters. The three methods are implemented using different optimization algorithms to optimize the choice of the coefficients of the three filters. This optimization is done to approximate the frequency response of an ideal fractional operator. This comparison aims to determine each implementation method’s accuracy and resource usage level to decide which method is better for different systems. © 2021 IEEE.

Butterworth passive filter in the fractional-order

In this paper, the generalized analysis of the first Butterworth filter based on two passive elements is introduced in the fractional-order sense. The fractional-order condition of the Butterworth circuit is presented for the first time where it will lead us back to the known condition of the integer-order circuit when the two fractional-orders equal one. Therefore, the conventional behavior of the integer-order circuit is a narrow subset of the fractional-order ones. The circuit is studied under same and different order cases, and verified through their numerical simulations. Stability analysis is also introduced showing the poles location in the fractional-order versus integer order cases. © 2011 IEEE.

General procedure for two integrator loops fractional order oscillators with controlled phase difference

This paper studies the fractional order two integrator loop based sinusoidal oscillators with two fractional order elements of different orders. Two general cases have been discussed and closed forms for the oscillation frequency and oscillation condition are driven. In addition, the effect of the fractional orders on the phase difference between the two oscillatory outputs is also presented. Design procedure for the two general cases is illustrated with numerical examples and validated through circuit simulations for three examples of oscillators based on two integrator loops. © 2013 IEEE.

CCII based KHN fractional order filter

This work aims to generalize the analysis of the fractional order filter to work for the low-pass, band-pass and high-pass responses. So, general expression for the maximum and minimum frequency points and the half power frequency points will be derived. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced. Besides, the effect of the fractional orders on the frequency response will be presented. Finally, to verify the numerical analysis and the proposed design procedure, circuit simulation will be used. © 2013 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.