The Design of Digital Fractional-order Differentiators and Integrators
Date Issued
2007
Date
2007
Author(s)
Fan, Ya-Tin
DOI
en-US
Abstract
In this thesis, we introduce a few designs of digital integrator, and a few designs of fractional-order differintegrator. We apply some numerical integration rules and fractional delay filters to obtain the closed form design of IIR digital integrators. There are three types of numerical integration rules to be investigated: Newton-Cotes quadrature rule, Gauss-Legendre quadrature rule and Clenshaw-Curtis quadrature rule. The fractional delay involved in the design will be implemented by FIR Lagrange and IIR allpass fractional delay filters. Also, a combined version is proposed. Several digital filter design examples are illustrated to demonstrate the effectiveness. Chapter 5 is to show the designs of the fractional-order differintegrator. We find a suitable generating function to fit the ideal fractional-order differintegrator. Then discretize the fractional-order with a power series expansion or continued fraction expansion. Last, we discuss the different methods to decrease the absolute magnitude error. Moreover, the filter properties will also be presented at the end of the chapter. Finally, we make a conclusion of this thesis and suggest the future work in chapter 6.
Subjects
數位積分器
數值積分法
分數階微積分器
數位化
數位微分器
連分數展開
Digital integrator
Numerical integration rule
fractional-order differintegrator
Discretization
Digital differentiator
Continued fraction expansion
Type
thesis
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