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Design of Fractional-Order Chebyshev Low-Pass Filter for Optimized Magnitude Response Using Metaheuristic Evolutionary Algorithms

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Abstract

The research work presented in this paper discusses the traditional methods of design of fractional-order filters and their shortcomings and proposes a method of deriving the physically realizable Chebyshev low-pass fractional-order filters of order (\(1+\alpha \)) which produce an optimum magnitude response. The filters of (\(1+\alpha \)) order are derived in terms of a rational transfer function of order \(N=3\). The proposed method utilizes different nature-inspired evolutionary metaheuristic algorithms which traverse the non-uniform, multidimensional, multimodal, nonlinear space and produce the coefficients of the polynomial for desired filters effectively. Comparisons are made between the reported literature and presented work on various key factors like robustness and magnitude errors in stopband and passband. It has been observed that the proposed work outperforms the work reported in the literature with minimum and maximum errors being \(-\) 58.9 dB and \(-\) 31.46 dB. SPICE implementations of the proposed filters by operational amplifiers (Op-Amps) and operational transconductance amplifiers (OTAs) have been shown. It is observed that the implemented filters closely follow the magnitude curve of ideal filters with a mean square errors of \(-\) 74.97 dB and \(-\) 70.94 dB for 1.5-order and \(-\) 69.81 dB and \(-\) 86.13 dB for 1.7-order filters for Op-Amp and OTA-based filters, respectively. This justifies the feasibility and accuracy of the proposed filters in practical environment.

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The data sets generated during and/or analysed during the current study are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors would like to acknowledge Prof. Harish Parthasarthy for his valuable guidance and continuous support during the work.

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  1. Electronics and Communication Engineering Department, Netaji Subhas University of Technology, New Delhi, 110078, India

    Ritu Daryani, Bhawna Aggarwal & Maneesha Gupta

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  1. Ritu Daryani
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Appendix A Pseudocodes for Algorithms

Appendix A Pseudocodes for Algorithms

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Daryani, R., Aggarwal, B. & Gupta, M. Design of Fractional-Order Chebyshev Low-Pass Filter for Optimized Magnitude Response Using Metaheuristic Evolutionary Algorithms. Circuits Syst Signal Process 42, 2507–2537 (2023). https://doi.org/10.1007/s00034-022-02227-9

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