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Design of Approximately Linear Phase Low Pass IIR Digital Differentiator using Differential Evolution Optimization Algorithm

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Abstract

In this paper, a new design approach of approximately linear phase infinite impulse response (IIR) low pass digital differentiator (LPDD) is proposed and studied. The proposed design is based on a transfer function that has a numerator with anti-symmetric coefficients. To better control the magnitude response of the designed LPDD, the differential evolution (DE) optimization algorithm is used to find the coefficients of the transfer function that meets an appropriate pass band and stop band edge frequencies. The use of appropriate pass band and stop band edge frequencies gives the designer of the LPDD direct control on the width of the transition band. The designed LPDD using the proposed approach has approximately linear phase and much better magnitude response than that of the IIR LPDDs designed using other techniques reported in literature. In addition, the designed LPDD using the proposed approach has steeper roll-off magnitude response and narrower transition band than that of designed IIR and high order FIR LPDDs available in the literature.

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References

  1. J. Ababneh, T. Aldalgamouni, A. Alqudah, Minimum bit error rate multiuser detection of SDMA-OFDM system using differential evolutionary algorithm, In Proceedings of the 6th IEEE International Conference on Wireless and Mobile Computing, Networking and Communications. Niagara Falls, Canada, Oct. (2010)

  2. A. Aggarwal, M. Kumar, T. Rawat, Design of digital differentiator using the L1-method and swarm intelligence-based optimization algorithms. Arab. J. Sci. Eng. 44(3), 1917–1931 (2018)

    Article  Google Scholar 

  3. A. Aggarwal, T.K. Rawat, M. Kumar, D.K. Upadhyay, Efficient design of digital FIR differentiator using L1-method. Radio Eng. 25(2), 86–92 (2016)

    Google Scholar 

  4. A. Aggarwal, T.K. Rawat, D.K. Upadhyay, Optimal design of L1-norm based IIR digital differentiators and integrators using the bat algorithm. IET Signal Proc. 11(1), 26–35 (2016)

    Article  Google Scholar 

  5. M.A. Al-Alaoui, Linear phase low-pass IIR digital differentiators. IEEE Trans. Signal Process. 55(2), 697–706 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. M.A. Al-Alaoui, Class of digital integrators and differentiators. IET Signal Proc. 5(2), 251–260 (2011)

    Article  Google Scholar 

  7. M. A. Al-Alaoui, M. Baydoun, Novel wideband digital differentiators and integrators using different optimization techniques, In Proceedings of the International Symposium on Signals, Circuits and Systems (ISSCS), Iasi, Romania July (2013) pp. 1–4

  8. Z. Albataineh, J. Ababneh, F. Salem, Linear phase FIR low pass filter design using hybrid-differential evolution. Int. J. Res. Wirel. Syst. 1(2), 43–49 (2012)

    Google Scholar 

  9. T.A.A. Ali, Z. Xiao, J. Sun, S. Mirjalili, V. Havyarimana, H. Jiang, Optimal design of IIR wideband digital differentiators and integrators using salp swarm algorithm. Knowl.-Based Syst. 182, 104834 (2019)

    Article  Google Scholar 

  10. L. Grossmann, Y. Eldar, An L1-method for the design of linear-phase FIR digital filters. IEEE Trans. Signal Process. 55(11), 5253–5266 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Gupta, M. Jain, B. Kumar, Novel class of stable wideband recursive digital integrators and differentiators. IET Signal Proc. 4(5), 560–566 (2010)

    Article  Google Scholar 

  12. M. Gupta, B. Relan, R. Yadav, V. Aggarwal, Wideband digital integrators and differentiators designed using particle swarm optimisation. IET Signal Proc. 8(6), 668–679 (2014)

    Article  Google Scholar 

  13. Z. He, Y. Sun, Design of low-pass digital differentiators based on B-splines. Signal Processing: An International Journal. 8(3), 30–42 (2014)

    Google Scholar 

  14. E.C. Ifeachor, B.W. Jervis, Digital Signal Processing (Prentice-Hall, New Jersy, 2002).

    Google Scholar 

  15. M. Jain, M. Gupta, N. Jain, Linear phase second order recursive digital integrators and differentiators. Radio Eng. 21(2), 712–717 (2012)

    Google Scholar 

  16. J.F. Kaiser, Digital filters, in System analysis by digital filters. ed. by F. Kuo, J.F. Kaiser (Wiley, NewYork, 1966)

    Google Scholar 

  17. D. Karaboǧa, S. Ökdem, A simple and global optimization algorithm for engineering problems: differential evolution algorithm. Turk. J. Elec. Eng. 12(1), 53–60 (2004)

    Google Scholar 

  18. A. Krubowski, I. Kale, Almost linear –phase poly phase IIR low pass /high pass filter approach. In Proceedings of the International Symposium on Signal Processing Applications (ISSPA), Brisbane, Australia, Aug. (1999) pp. 969–972

  19. M. Kumar, T.K. Rawat, Optimal design of FIR fractional order differentiator using cuckoo search algorithm. Expert Syst. Appl. 42(7), 3433–3449 (2015)

    Article  Google Scholar 

  20. B. Kumar, S.C.D. Roy, H. Shah, On the design of FIR digital differentiators which are maximally linear at the frequency pi/p, p in {positive integers}. IEEE Trans. Signal Process. 40(9), 2334–2338 (1992)

    Article  Google Scholar 

  21. B. Kumar, S.C.D. Roy, Coefficients of maximally linear FIR digital differentiators for low frequencies. Electron. Lett. 24(9), 563–565 (1988)

    Article  Google Scholar 

  22. B. Kumar, S.C.D. Roy, Design of digital differentiators for low frequencies. Proc. IEEE. 76(3), 287–289 (1988)

    Article  Google Scholar 

  23. A. Kurosu, S. Miyase, S. Tomiyama, T. Takebe, A technique to truncate IIR filter impulse response and its application to real time implementation of linear–phase IIR filters. IEEE Trans. Signal Process. 51(5), 1284–1292 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  24. L. Li, L. Xie, W.Y. Yan, Y.C. Soh, Design of low order linear phase IIR filters via orthogonal projection. IEEE Trans. Signal Process. 47(2), 448–457 (1999)

    Article  Google Scholar 

  25. J.S. Lim, Two Dimensional Signal and Image Processing (Prentice-Hall, New Jersy, 1990).

    Google Scholar 

  26. S.J. Maeng, B.G. Lee, A design of linear phase IIR Nyquist filters. IEEE Trans. Sel. Areas Commun. 13(1), 167–175 (1995)

    Article  Google Scholar 

  27. S. Mahata, S.K. Saha, R. Kar, D. Mandal, Optimal design of wideband digital integrators and differentiators using harmony search algorithm. Int. J. Numer. Model. Electron. Netw. Devices Fields 30(5), 1–20 (2016)

    Google Scholar 

  28. S. Mahata, S.K. Saha, R. Kar, D. Mandal, Optimal design of wideband digital integrators and differentiators using hybrid flower pollination algorithm. Soft. Comput. 22(11), 3757–3783 (2017)

    Article  Google Scholar 

  29. MATLAB is a registered trademark of MathWorks, Inc. https://www.mathworks.com.

  30. R. Mikhael, P. Agathoblis, C. Xiao, Design of linear phase recursive filters by optimization of model reduced non recursive filters. In Proceedings of the PACRIM, Victoria, B.C., Canada, Aug. (2003) pp. 94–97.

  31. S. Mirjalili, S.M. Mirjalili, A. Lewis, Grey Wolf Optimizer. Adv. Eng. Softw. 69, 46–61 (2014)

    Article  Google Scholar 

  32. C. Nayak, S.K. Saha, R. Kar, D. Mandal, Optimal SSA-based wideband digital differentiator design for cardiac QRS complex detection application. Int. J. Numer. Modell.: Electron. Netw. Devices Fields (2018). https://doi.org/10.1002/jnm.2524

    Article  Google Scholar 

  33. C. Nayak, S.K. Saha, R. Kar, D. Mandal, An Efficient QRS Complex Detection Using Optimally Designed Digital Differentiator. Circuits Syst. Signal Process. 38, 716–749 (2019)

    Article  Google Scholar 

  34. N.Q. Ngo, A new approach for the design of wideband digital integrator and differentiator. IEEE Trans. Circuits Syst., II Exp. Briefs 53(9), 936–940 (2006)

    Article  Google Scholar 

  35. R.C. Nongpiur, D.J. Shpak, A. Antoniou, Design of IIR digital differentiators using constrained optimization. IEEE Trans. Signal Process. 62(7), 1729–1739 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  36. J. Pan, W.J. Tompkins, A real-time QRS detection algorithm. IEEE Trans. Biomed. Eng. 32, 230–236 (1985)

    Article  Google Scholar 

  37. S.R. Powell, P.M. Chau, A technique for realizing linear phase IIR filters. IEEE Trans. Signal Process. 19(11), 2425–2435 (1991)

    Article  Google Scholar 

  38. E. Rashedi, H. Nezamabadi-pour, S. Saryazdi, GSA a gravitational search algorithm. Inf. sci. 179(13), 2232–2248 (2009)

    Article  MATH  Google Scholar 

  39. I. Selesnick, Maximally flat lowpass digital differentiators. IEEE Trans. Circuits Syst. II. 49(3), 219–223 (2002)

    Article  Google Scholar 

  40. Y. Shi, R. Eberhart, Parameter selection in particle swarm optimization. In Proceedings of the Evolutionary Programming VII (EP98), March (1998), pp. 591–600

  41. M.L. Skolnik, Introduction to Radar Systems (McGraw-Hill, NewYork, 1980).

    Google Scholar 

  42. V. Sreeram, P. Agathoblis, Design of a linear phase IIR filters via impulse-response Gramians. IEEE Trans. Signal Process. 40(2), 389–394 (1992)

    Article  Google Scholar 

  43. R. Storn, K. Price, Differential evolution-A simple and efficient heuristic for global Optimization over continuous spaces. J. Global Optim. 11, 341–359 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  44. R. Storn, Differential evolution design of an IIR-filter. In Proceedings of the IEEE International Conference on Evolutionary Computation, Nayoya, Japan, May (1996) pp. 268–273

  45. A. Tahmasbi, S. B. Shokouhi, New Optimised IIR Low-Pass Differentiators. In Proceedings of the International Conference on Signal Acquisition and Processing, Bangalore, India, Feb. (2010) pp. 205–209

  46. C.C. Tseng, Stable IIR differentiator design using iterative quadratic programming approach. Signal Process. 80(5), 857–866 (2000)

    Article  MATH  Google Scholar 

  47. D.K. Upadhyay, R.K. Singh, Recursive wideband digital differentiator and integrator. Electron. Lett. 47(11), 647–648 (2011)

    Article  Google Scholar 

  48. D.K. Upadhyay, Class of recursive wideband digital differentiators and integrators. Radio Eng. 21(3), 904–910 (2012)

    Google Scholar 

  49. D.K. Upadhyay, Recursive wideband digital differentiators. Electron. Lett. 46(25), 1661–1662 (2010)

    Article  Google Scholar 

  50. S. Usui, I. Amidror, Digital low-pass differentiation for biological signal processing. IEEE Trans. Biomed. Eng. 29, 686–693 (1982)

    Article  Google Scholar 

  51. A. Wolfram, O. Moseler, Design and Application of Digital FIR Differentiators Using Modulating Functions. IFAC Proc. Volumes. 33(15), 1037–1042 (2000)

    Article  Google Scholar 

  52. C. Xiao, J. C. Olivier, P. Agathoklis, Design of linear phase IIR filters via weighted least-squares approximations. In Proceedings of the IEEE International Conference on Acoustics, Speech, Signal Processing (ICASSP), Salt Lake City, UT, May (2001) pp. 3817–3820.

  53. X. S. Yang, S. Deb, Cuckoo search via Lévy flights. In Proceedings of the World Congress on Nature and Biologically Inspired Computing (NaBIC), Dec. (2009), pp. 210–214

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  1. Department of Electrical Engineering, Jordan University of Science and Technology, Irbid, 22110, Jordan

    Jehad Ababneh & Majid Khodier

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  1. Jehad Ababneh
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Ababneh, J., Khodier, M. Design of Approximately Linear Phase Low Pass IIR Digital Differentiator using Differential Evolution Optimization Algorithm. Circuits Syst Signal Process 40, 5054–5076 (2021). https://doi.org/10.1007/s00034-021-01710-z

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