Skip to main content
Springer Nature Link
Log in

Double Exponent Fractional-Order Filters: Approximation Methods and Realization

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

The main goal of this work is to exploit different tools in order to approximate a general double exponent fractional-order transfer function. Through the appropriate selection of the two fractional orders of this function, different types of filters can be derived. The investigated approximation tools are either curve fitting based tools or the Padé approximation tool, and the derived approximated transfer functions in all cases have the form of rational integer-order polynomials, which can be easily realized electronically.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. A.M. AbdelAty, A.S. Elwakil, A.G. Radwan, C. Psychalinos, B. Maundy, Approximation of the fractional-order Laplacian s\(^{\alpha }\) as a weighted sum of first-order high-pass filters. IEEE Trans. Circuits Syst. II Express Briefs 65(8), 1114–1118 (2018)

    Article  Google Scholar 

  2. A.S. Ali, A.G. Radwan, A.M. Soliman, Fractional order Butterworth filter: active and passive realizations. IEEE J. Emerg. Selected Topics Circuits Syst. 3(3), 346–354 (2013)

    Article  Google Scholar 

  3. K. Bingi, R. Ibrahim, M.N. Karsiti, S.M. Hassam, V.R. Harindran, Frequency response based curve fitting approximation of fractional-order PID controllers. Int. J. Appl. Math. Comput. Sci. 29(2), 311–326 (2019)

    Article  MathSciNet  Google Scholar 

  4. K. Bingi, R. Ibrahim, M.N. Karsiti, S.M. Hassan, V.R. Harindran, Fractional-order Systems and PID Controllers: Using Scilab and Curve Fitting Based Approximation Techniques (Springer, Berlin, 2019)

    MATH  Google Scholar 

  5. T.J. Freeborn, B. Maundy, A. Elwakil, Fractional resonance-based \({RL}_{\beta }{C}_{\alpha }\) filters. Math. Prob. Eng. (2013). https://doi.org/10.1155/2013/726721

    Article  MathSciNet  MATH  Google Scholar 

  6. A.M. Hassanein, A. Soltan, L.A. Said, A.H. Madian, A.G. Radwan Analysis and design of fractional-order low-pass filter with three elements of independent orders. In: 2019 Novel Intelligent and Leading Emerging Sciences Conference (NILES), vol. 1 (IEEE, 2019) pp. 218–221

  7. S. Kapoulea, G. Tsirimokou, C. Psychalinos, A.S. Elwakil, Employment of the Padé approximation for implementing fractional-order lead/lag compensators. AEU Int. J. Electron. Commun. 120, 153203 (2020)

    Article  Google Scholar 

  8. B. Krishna, Studies on fractional order differentiators and integrators: a survey. Sig. Process. 91(3), 386–426 (2011)

    Article  Google Scholar 

  9. L. Lorentzen, Padé approximation and continued fractions. Appl. Numer. Math. 60(12), 1364–1370 (2010)

    Article  MathSciNet  Google Scholar 

  10. A. Oustaloup, F. Levron, B. Mathieu, F.M. Nanot, Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 47(1), 25–39 (2000)

    Article  Google Scholar 

  11. A.A. Ozdemir, S. Gumussoy, Transfer function estimation in system identification toolbox via vector fitting. IFAC-PapersOnLine 50(1), 6232–6237 (2017)

    Article  Google Scholar 

  12. A.G. Radwan, A.S. Elwakil, A.M. Soliman, On the generalization of second-order filters to the fractional-order domain. J. Circuits Syst. Computers 18(02), 361–386 (2009)

    Article  Google Scholar 

  13. A.G. Radwan, A.M. Soliman, A.S. Elwakil, First-order filters generalized to the fractional domain. J Circuits Syst. Computers 17(01), 55–66 (2008)

    Article  Google Scholar 

  14. A. Soltan, A.G. Radwan, A.M. Soliman, Fractional order filter with two fractional elements of dependant orders. Microelectron. J. 43(11), 818–827 (2012)

    Article  Google Scholar 

  15. G. Tsirimokou, A systematic procedure for deriving RC networks of fractional-order elements emulators using MATLAB. AEU-Int. J. Electron. Commun. 78, 7–14 (2017)

    Article  Google Scholar 

  16. G. Tsirimokou, C. Psychalinos, A.S. Elwakil, Fractional-order electronically controlled generalized filters. Int. J. Circuit Theory Appl. 45(5), 595–612 (2017)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Electronics Laboratory, Physics Department, University of Patras, 26504, Rio Patras, GR, Greece

    Stavroula Kapoulea & Costas Psychalinos

  2. Department of Electrical and Computer Engineering, University of Sharjah, P. O. Box 27272, Sharjah, United Arab Emirates

    Ahmed S. Elwakil

  3. Nanoelectronics Integrated Systems Center (NISC), Nile University, Giza, Egypt

    Ahmed S. Elwakil

  4. Department of Electrical and Computer Engineering, University of Calgary, Alberta, Canada

    Ahmed S. Elwakil

Authors
  1. Stavroula Kapoulea
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Costas Psychalinos
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Ahmed S. Elwakil
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Costas Psychalinos.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This research is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme “Human Resources Development, Education and Lifelong Learning” in the context of the project “Strengthening Human Resources Research Potential via Doctorate Research-2nd Cycle” (MIS-5000432), implemented by the State Scholarships Foundation (IKY).

This article is based upon work from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kapoulea, S., Psychalinos, C. & Elwakil, A.S. Double Exponent Fractional-Order Filters: Approximation Methods and Realization. Circuits Syst Signal Process 40, 993–1004 (2021). https://doi.org/10.1007/s00034-020-01514-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-020-01514-7

Keywords