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Optimal Approximation of Fractional-Order Butterworth Filter Based on Weighted Sum of Classical Butterworth Filters
- Source :
- IEEE Access, Vol 9, Pp 81097-81114 (2021)
- Publication Year :
- 2021
- Publisher :
- IEEE, 2021.
-
Abstract
- In this paper, a new two-steps design strategy is introduced for the optimal rational approximation of the fractional-order Butterworth filter. At first, the weighting factors of the summation between the ${n}^{\text {th}}$ -order and the $(n + 1)^{\text {th}}$ -order Butterworth filters are optimally determined. Subsequently, this model is employed as an initial point for another optimization routine, which minimizes the magnitude-frequency error relative to the $(n+\alpha)^{\text {th}}$ -order, where $\alpha \in (0, 1)$ , Butterworth filter. The proposed approximant demonstrates improved performance about the magnitude mean squared error compared to the state-of-the-art design for six decades of bandwidth, but the introduced approach does not require a fractional-order transfer function model and the approximant of the $s^\alpha $ operator. The proposed strategy also avoids the use of the cascading technique to yield higher-order fractional-order Butterworth filter models. The performance of the proposed $1.5^{\text {th}}$ -order Butterworth filter in follow-the-leader feedback topology is verified through SPICE simulations and its hardware implementation based on Analog Devices AD844AN-type current feedback operational amplifier.
Details
- Language :
- English
- ISSN :
- 21693536
- Volume :
- 9
- Database :
- Directory of Open Access Journals
- Journal :
- IEEE Access
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.2a8cee4af1824b7695fe677c26c488bf
- Document Type :
- article
- Full Text :
- https://doi.org/10.1109/ACCESS.2021.3085515