Skip to main content
SpringerLink
Log in

Optimal designs of analogue and digital fractional order filters for signal processing applications

  • S.I. : Visvesvaraya
  • Published:
CSI Transactions on ICT Aims and scope Submit manuscript

Abstract

Our initial research work was focussed on employing metaheuristic optimization techniques to design optimal digital signal processing (DSP) systems such as the full band, conventional infinite impulse response differentiators and integrators meeting the accurate magnitude responses with a smaller average group delay. Since, integer order systems are a tight subset of the fractional order (FO) systems the research has been extended towards the optimal design of FO differentiators and integrators in the discrete domain with improved frequency response performances. Specific emphasis was laid on the feasibility of the designed FO differentiators in controlling a double-integrator plant. Analogue Butterworth filter with fractional stepping in the transition band has also been realized using an optimal integer-order rational transfer function. In future, we intend to design and implement generalized fractional-order filters on FPGA/DSP kit and FPAAs.

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

Access this article

Log in via an institution

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
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Mahata S, Saha SK, Kar R, Mandal D (2017) Enhanced colliding bodies optimisation-based optimal design of wideband digital integrators and differentiators. Int J Bio-Inspired Comput 9:165–181

    Article  Google Scholar 

  2. Mahata S, Saha SK, Kar R, Mandal D (2016) Optimal design of wideband digital integrators and differentiators using harmony search algorithm. Int J Numer Model Electron Netw Dev Fields. https://doi.org/10.1002/jnm.2203

    Article  Google Scholar 

  3. Mahata S, Saha SK, Kar R, Mandal D (2018) Optimal design of wideband digital integrators and differentiators using hybrid flower pollination algorithm”. Soft Comput 22:3757–3783

    Article  Google Scholar 

  4. Al-Alaoui MA (2011) Class of digital integrators and differentiators. IET Signal Process 5:251–260

    Article  Google Scholar 

  5. Jalloul MK, Al-Alaoui MA (2015) Design of recursive digital integrators and differentiators using particle swarm optimization. Int J Circuit Theor Appl 44:948–967

    Article  Google Scholar 

  6. Mahata S, Saha SK, Kar R, Mandal D (2017) Optimal and accurate design of fractional order digital differentiator—and evolutionary approach. IET Signal Process 11:181–196

    Article  Google Scholar 

  7. Mahata S, Saha SK, Kar R, Mandal D (2018) Optimal design of fractional order digital differentiator using flower pollination algorithm. J Circuits Syst Comput 27:1–35

    Article  Google Scholar 

  8. Mahata S, Saha SK, Kar R, Mandal D (2018) A metaheuristic optimization approach to discretize the fractional order Laplacian operator without employing a discretization operator. Swarm Evolut Comput. https://doi.org/10.1016/j.swevo.2018.06.007

    Article  Google Scholar 

  9. Mahata S, Saha SK, Kar R, Mandal D (2016) Optimal design of wideband infinite impulse response fractional order digital integrators using colliding bodies optimisation algorithm. IET Signal Process 10:1135–1156

    Article  Google Scholar 

  10. Mahata S, Saha SK, Kar R, Mandal D (2018) Optimal design of wideband fractional order digital integrators using symbiotic organisms search algorithm. IET Circuit Devices Syst 12:362–373

    Article  Google Scholar 

  11. Rana KPS, Kumar V, Garg Y et al (2016) Efficient design of discrete fractional order differentiators using Nelder–Mead simplex algorithm. Circuits Syst Signal Process 35:2155–2188

    Article  Google Scholar 

  12. Gupta M, Yadav R (2014) New improved fractional order differentiator models based on optimized digital differentiators. Sci World J 2014:1–11

    Google Scholar 

  13. Leulmi F, Ferdi Y (2015) Improved digital rational approximation of the operator sα using second-order s-to-z transform and signal modelling. Circuits Syst Signal Process 34:1869–1891

    Article  Google Scholar 

  14. Gupta M, Yadav R (2013) Optimization of integer order integrators for deriving improved models of their fractional counterparts. J Optim 2013:1–11

    Google Scholar 

  15. Yadav R, Gupta M (2015) New improved fractional order integrators using PSO optimization. Int J Electron 102:490–499

    Article  Google Scholar 

  16. Mahata S, Saha SK, Kar R, Mandal D (2018) Optimal design of fractional order low pass Butterworth filter with accurate magnitude response. Digit Signal Process 72:96–114

    Article  Google Scholar 

  17. Mahata S, Saha SK, Kar R, Mandal D (2018) Accurate integer order rational approximation of fractional order low pass Butterworth filter using a metaheuristics optimization approach. IET Signal Process 12:581–589

    Article  Google Scholar 

  18. Mahata S, Saha SK, Kar R, Mandal D (2018) Approximation of fractional-order low pass filter. IET Signal Process 12:123–145. https://doi.org/10.1049/iet-spr.2018.5128

    Article  Google Scholar 

  19. Freeborn TJ, Maundy B, Elwakil AS (2010) Field-programmable analogue array implementation of fractional step filters. IET Circuits Devices Syst 4(6):514–524

    Article  Google Scholar 

  20. Psychalinos C, Tsirimokou G, Elwakil AS (2016) Switched-capacitor fractional-step Butterworth filter design. Circuits Syst Signal Process 35(4):1377–1393

    Article  MathSciNet  Google Scholar 

  21. Freeborn TJ (2016) Comparison of (1 + α) fractional-order transfer functions to approximate low pass Butterworth magnitude responses. Circuits Syst Signal Process 35(6):1983–2002

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronics and Communication Engineering, National Institute of Technology, Durgapur, Durgapur, India

    Rajib Kar

Authors
  1. Rajib Kar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rajib Kar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kar, R. Optimal designs of analogue and digital fractional order filters for signal processing applications. CSIT 7, 175–180 (2019). https://doi.org/10.1007/s40012-019-00225-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40012-019-00225-y

Keywords

Search

Navigation