Skip to main content
SpringerLink
Log in

A New Method for Designing of Stable Digital IIR Filter Using Hybrid Method

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

Abstract

In this paper, a new technique for designing of a stable digital infinite impulse response filter, with improved performance in passband and stopband regions using quantum particle swarm optimization (QPSO) and artificial bee colony (ABC) algorithm, is explored in frequency domain. In the proposed method, QPSO technique is modified with exploiting the novelty of search and replacement mechanism of scout bee from ABC algorithm. For this purpose, a new design problem is constructed as a nonlinear minimization of mean square error between the designed and desired filter responses in passband, stopband, and transition band simultaneously, allowing permissible ripples in passband and stopband. Efficiency of the proposed technique is measured by several attributes like passband error, stopband error, total squared error (SE), maximum stopband attenuation, maximum passband error \( \left( {e_{pb}^{\hbox{max} } } \right) \), passband ripple, and maximum phase deviation in passband. Experimental results evidence that a significant reduction is achieved in sum of the SE in passband and stopband from 12 to 54%, and the performance is not degraded due to quantization and truncation process. However, computation time in term of CPU time is increased from 0.77 to 4.1%, along with 2.62–7.43% hike in number of function evaluation, when compared to QPSO. A comparative study reveals that the proposed method yields better fidelity parameter as compared other evolutionary algorithms such as gravitational search algorithm, genetic algorithm, and variants of PSO. The proposed technique is also suitable for higher filter taps.

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
Fig. 15

Similar content being viewed by others

References

  1. N. Agrawal, A. Kumar, V. Bajaj, Design of digital IIR filter with low quantization error using hybrid optimization technique. Soft. Comput. 22(9), 2253–2971 (2017)

    Google Scholar 

  2. M.K. Ahirwal, A. Kumar, G.K. Singh, Adaptive filtering of EEG/ERP through bounded range artificial bee colony (BR-ABC) algorithm. Digit. Signal Process. 25, 164–172 (2014)

    Article  Google Scholar 

  3. M.K. Ahirwal, A. Kumar, G.K. Singh, EEG/ERP adaptive noise canceller design with controlled search space (CSS) approach in cuckoo and other optimization algorithms. IEEE/ACM Trans. Comput. Biol. Bioinform. 10(6), 1491–1504 (2013)

    Article  Google Scholar 

  4. A. Antoniou, Digital Filters: Analysis, Design, and Applications (McGraw-Hil, New York, 2000)

    Google Scholar 

  5. S. Chen, B.L. Luk, Adaptive simulated annealing for optimization in signal processing applications. Sig. Process. 79(1), 117–128 (1999)

    Article  MATH  Google Scholar 

  6. A. Chottera, G. Jullien, A linear programming approach to recursive digital filter design with linear phase. IEEE Trans. Circuits Syst. 29(3), 139–149 (1982)

    Article  Google Scholar 

  7. M. Dorigo, V. Maniezzo, A. Colorni, M. Dorigo, Positive Feedback as a Search Strategy. Technical Report 91–016 (1991), p. 1–20

  8. D.M. Etter, M. Hicks, K. Cho, Recursive adaptive filter design using an adaptive genetic algorithm, in IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP (1982), p. 635–638

  9. L. Fang, Z. Zhiguang, An improved QPSO algorithm and its application in the high-dimensional complex problems. Chemom. Intell. Lab. Syst. 132, 82–90 (2014)

    Article  Google Scholar 

  10. C.Y.F. Ho, B.W.K. Ling, Y.Q. Liu, P.K.S. Tam, K.L. Teo, Optimal design of magnitude responses of rational infinite impulse response filters. IEEE Trans. Signal Process. 54(10), 4039–4046 (2006)

    Article  MATH  Google Scholar 

  11. A. Jiang, H.K. Kwan, Minimax design of IIR digital filters using iterative SOCP. IEEE Trans. Circuits Syst. I Regul. Pap. 57(6), 1326–1337 (2010)

    Article  MathSciNet  Google Scholar 

  12. N. Karaboga, F. Latifoglu, Elimination of noise on transcranial Doppler signal using IIR filters designed with artificial bee colony—ABC-algorithm. Digit. Signal Process. 23(3), 1051–1058 (2013)

    Article  MathSciNet  Google Scholar 

  13. D. Karaboga, B. Akay, A comparative study of artificial bee colony algorithm. Appl. Math. Comput. 214(1), 108–132 (2009)

    MathSciNet  MATH  Google Scholar 

  14. N. Karaboga, A new design method based on artificial bee colony algorithm for digital IIR filters. J. Frankl. Inst. 346(4), 328–348 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. N. Karaboga, B. Cetinkaya, Design of digital FIR filters using differential evolution algorithm. Circuits Syst. Signal Process. 25(5), 649–660 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. N. Karaboga, Digital IIR filter design using differential evolution algorithm. EURASIP J. Adv. Signal Process. 2005(8), 1269–1276 (2005)

    Article  MATH  Google Scholar 

  17. N. Karaboğa, B. Çetinkaya, Efficient design of fixed point digital FIR filters by using differential evolution algorithm, in Lecture Notes in Computer Science, ed. by J.C. Alberto, P.F. Sandoval (Springer, Berlin, 2005), p. 812–819

    Google Scholar 

  18. A. Kalinli, N. Karaboga, A new method for adaptive IIR filter design based on tabu search algorithm. AEU Int. J. Electron. Commun. 59(2), 111–117 (2005)

    Article  MATH  Google Scholar 

  19. N. Karaboga, A. Kalinli, D. Karaboga, Designing digital IIR filters using ant colony optimisation algorithm. Eng. Appl. Artif. Intell. 17(3), 301–309 (2004)

    Article  MATH  Google Scholar 

  20. N. Karaboga, B. Cetinkaya, Performance comparison of genetic and differential evolution algorithms for digital FIR filter design, in Lecture Notes in Computer Science, ed. by T. Yakhno (Springer, Berlin, 2004), p. 482–488

    Google Scholar 

  21. J. Kennedy, R. Eberhart, Particle swarm optimization, in IEEE International Conference on Neural Networks (1995), p. 1942–1948

  22. P. Lagos-Eulogio, J.C. Seck-Tuoh-Mora, N. Hernandez-Romero, J. Medina-Marin, A new design method for adaptive IIR system identification using hybrid CPSO and DE. Nonlinear Dyn. 88(4), 2371–2389 (2017)

    Article  Google Scholar 

  23. M.C. Lang, Least-squares design of IIR filters with prescribed magnitude and phase responses and a pole radius constraint. Signal Process. IEEE Trans. 48(11), 3109–3121 (2000)

    Article  Google Scholar 

  24. W.S. Lu, Design of stable minimax IIR digital filters using semidefinite programming, in IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353) (2000), p. 355–358

  25. W.S. Lu, Design of stable IIR digital filters with equiripple passbands and peak-constrained least-squares stopbands. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 46(11), 1421–1426 (1999)

    Article  Google Scholar 

  26. W.S. Lu, S.C. Pei, C.C. Tseng, A weighted least-squares method for the design of stable 1-D and 2-D IIR digital filters. IEEE Trans. Signal Process. 46(1), 1–10 (1998)

    Article  Google Scholar 

  27. S. Mahata, S.K. Saha, R. Kar, D. Mandal, Optimal design of fractional-order digital differentiator using flower pollination algorithm. J. Circuits Syst. Comput. 27(8), 1850129–1850135 (2017)

    Article  Google Scholar 

  28. A. Ouadi, H. Bentarzi, A. Recioui, Optimal multiobjective design of digital filters using spiral optimization technique. Springerplus 2, 461 (2013)

    Article  Google Scholar 

  29. S.T. Pan, Evolutionary computation on programmable robust IIR filter pole-placement design. IEEE Trans. Instrum. Meas. 60(4), 1469–1479 (2011)

    Article  Google Scholar 

  30. S.M. Rafi, A. Kumar, G.K. Singh, An improved particle swarm optimization method for multirate filter bank design. J. Frankl. Inst. 350(4), 757–769 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  31. S.K. Saha, R. Kar, D. Mandal, S.P. Ghoshal, Gravitation search algorithm: application to the optimal IIR filter design. J. King Saud Univ. Eng. Sci. 26(1), 69–81 (2014)

    Google Scholar 

  32. S.K. Saha, R. Kar, D. Mandal, S.P. Ghoshal, An efficient craziness based particle swarm optimization technique for optimal IIR filter design, in Transactions on Computational Science, ed. by M.L. Gavrilova, C.J.K. Tan, A. Abraham (Springer, Berlin, 2013), pp. 230–252

    Chapter  Google Scholar 

  33. S.K. Saha, R. Kar, D. Mandal, S.P. Ghoshal, Optimal IIR filter design using novel particle swarm optimization technique. Int. J. Circuits Syst. Signal Process. 6(2), 152–162 (2012)

    Google Scholar 

  34. S.K. Saha, S. Sarkar, R. Kar, D. Mandal, S. P. Ghoshal, Digital stable IIR low pass filter optimization using particle swarm optimization with improved inertia weight, in Ninth International Conference on Computer Science and Software Engineering, JCSSE (2012), p. 147–152

  35. A. Sarangi, S. Kumar, S. Kumari, S. Prasada, B. Ketan, Swarm intelligence based techniques for digital filter design. Appl. Soft Comput. J. 25, 530–534 (2014)

    Article  Google Scholar 

  36. I. Sharma, A. Kumar, G.K. Singh, Adjustable window based design of multiplier-less cosine modulated filter bank using swarm optimization algorithms. AEU Int. J. Electron. Commun. 70(1), 85–94 (2016)

    Article  Google Scholar 

  37. C. Sheng, L.L. Bing, Digital IIR filter design using particle swarm optimisation. Int. J. Modell. Identif. Control 9(4), 327–335 (2010)

    Article  Google Scholar 

  38. Y. Shi, R. Eberhart, A modified particle swarm optimizer, in 1998 IEEE International Conference on Computational Intelligence Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (1998), p. 69–73

  39. D.S. Sidhu, J.S. Dhillon, D. Kaur, Hybrid heuristic search method for design of digital IIR filter with conflicting objectives. Soft. Comput. 21(12), 3461–3476 (2017)

    Article  MATH  Google Scholar 

  40. J. Sun, X. Wu, V. Palade, W. Fang, C.H. Lai, W. Xu, Convergence analysis and improvements of quantum-behaved particle swarm optimization. Inf. Sci. (Ny) 193, 81–103 (2012)

    Article  MathSciNet  Google Scholar 

  41. J. Sun, B. Feng, W. Xu, Particle swarm optimization with particles having quantum behavior, in Congress on Evolutionary Computation,. CEC2004 (2004), p. 325–331

  42. K.S. Tang, K.F. Man, S. Kwong, Z.F. Liu, Design and optimization of IIR filter structure using hierarchical genetic algorithms. IEEE Trans. Ind. Electron. 45(3), 481–487 (1998)

    Article  Google Scholar 

  43. C.W. Tsai, C.H. Huang, C.L. Lin, Structure-specified IIR filter and control design using real structured genetic algorithm. Appl. Soft Comput. 9(4), 1285–1295 (2009)

    Article  Google Scholar 

  44. J.T. Tsai, J.H. Chou, T.K. Liu, Optimal design of digital IIR filters by using hybrid taguchi genetic algorithm. IEEE Trans. Ind. Electron. 53(3), 867–879 (2006)

    Article  Google Scholar 

  45. Y. Wang, B. Li, Y. Chen, Digital IIR filter design using multi-objective optimization evolutionary algorithm. Appl. Soft Comput. 11(2), 1851–1857 (2011)

    Article  Google Scholar 

  46. F. Wei, S. Jun, X. Wenbo, Design IIR digital filters using quantum-behaved particle swarm optimization, in International Conference on Natural Computation Advances in Natural Computing (2006), p. 637–640

  47. M. Xi, J. Sun, W. Xu, An improved quantum-behaved particle swarm optimization algorithm with weighted mean best position. Appl. Math. Comput. 205(2), 751–759 (2008)

    MATH  Google Scholar 

  48. L. Xue, Z. Rongchun, W. Qing, Optimizing the design of IIR filter via genetic algorithm, in International Conference on Neural Networks and Signal Processing (2003), p. 476–479

  49. X.S. Yang, Flower pollination algorithm for global optimization, in Unconventional Computation and Natural Computation (2012), pp. 240–250

  50. Y. Yu, Y. Xinjie, Cooperative coevolutionary genetic algorithm for digital IIR filter design. IEEE Trans. Ind. Electron. 54(3), 1311–1318 (2007)

    Article  Google Scholar 

  51. G. Zhang, W. Jin, F. Jin, Multi-criterion satisfactory optimization method for designing IIR digital filters, in International Conference on Communication Technology (2003), p. 1484–1490

Download references

Author information

Authors and Affiliations

  1. Discipline of Electronics and Communication Engineering, PDPM Indian Institute of Information Technology, Design and Manufacturing Jabalpur, Dumna Airport Road, Jabalpur, M. P., 482005, India

    N. Agrawal, A. Kumar & Varun Bajaj

Authors
  1. N. Agrawal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Varun Bajaj
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Kumar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Agrawal, N., Kumar, A. & Bajaj, V. A New Method for Designing of Stable Digital IIR Filter Using Hybrid Method. Circuits Syst Signal Process 38, 2187–2226 (2019). https://doi.org/10.1007/s00034-018-0959-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-018-0959-5

Keywords

Search

Navigation