Discrete-time signal processing (2nd ed.)
Discrete-time signal processing (2nd ed.)
A new IIR-type digital fractional order differentiator
Signal Processing - Special issue: Fractional signal processing and applications
Fractional differentiation for edge detection
Signal Processing - Special issue: Fractional signal processing and applications
Design of variable and adaptive fractional order FIR differentiators
Signal Processing - Fractional calculus applications in signals and systems
Time domain design of fractional differintegrators using least-squares
Signal Processing - Fractional calculus applications in signals and systems
IEEE Transactions on Signal Processing
Variable-order fractional derivatives and their numerical approximations
Signal Processing
IEEE Transactions on Circuits and Systems Part I: Regular Papers
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In this paper, the design problems of variable fractional order integrator and differentiator (FOID) are investigated. First, the transfer function of FOID is obtained by taking fractional power of the transfer function of conventional first order integrator and differentiator. Then, to implement this irrational transfer function, the logarithm and Taylor series expansion are used to get a realizable approximated rational function. The proposed implementation structure is similar to the conventional Farrow structure of fractional sample delay filter. Next, the proposed approach is applied to design fractional rectangular integrator, fractional trapezoidal integrator, fractional Simpson integrator, fractional Al-Alaoui differentiator and fractional maximally flat differentiator. Finally, design examples are demonstrated to illustrate the performance of the proposed design method.