Soft Computing

, Volume 22, Issue 9, pp 2953–2971 | Cite as

Design of digital IIR filter with low quantization error using hybrid optimization technique

Methodologies and Application

Abstract

In this paper, a hybrid optimization technique based on particle swarm optimization (PSO) and artificial bee colony (ABC) algorithm is presented for the optimal design of infinite impulse response (IIR) filter with low quantization effect. In this method, different variants of PSO have been exhaustively tested, and the time varying coefficients-PSO (TVC-PSO) is used to formulate a new hybrid technique for better exploitation and exploration, which is further modified by sorting and replacement mechanism of Scout Bee from ABC algorithm. For designing IIR filter, an objective function is constructed that satisfies the absolute error including peak ripples in passband and stopband regions in frequency domain, while stability of designed filter is confirmed by exploiting the lattice form structure during iterative computation that also reduces computation complexity. Several attributes such as passband error \((e_{\mathrm{p}})\), stopband error \((e_{\mathrm{s}})\), and stopband attenuation \((A_{\mathrm{s}})\) are used to measure the performance of proposed algorithm. The simulation results presented in this paper evidence that this technique can be effectively used for designing digital IIR filter with higher filter taps, and low quantization effect for fixed number of bits.

Keywords

Hybrid technique Evolutionary computation IIR Optimization Quantization 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Agrawal N, Kumar A, Bajaj V et al (2015a) Optimized design of digital IIR filter using artificial bee colony algorithm. In: 2015 International conference on signal processing, computing and control (ISPCC). IEEE, pp 316–321Google Scholar
  2. Agrawal N, Kumar A, Bajaj V et al (2015b) Hybrid method based optimized design of digital IIR filter. In: International conference on communication and signal processingGoogle Scholar
  3. Ahirwal MK, Kumar A, Singh GK (2013) EEG/ERP adaptive noise canceller design with controlled search space (CSS) approach in cuckoo and other optimization algorithms. IEEE/ACM Trans Comput Biol Bioinforma 10:1491–1504. doi: 10.1109/TCBB.2013.119 CrossRefGoogle Scholar
  4. Ahirwal MK, Kumar A, Singh GK (2014a) Adaptive filtering of EEG/ERP through Bounded Range Artificial Bee Colony (BR-ABC) algorithm. Digit Signal Process 25:164–172. doi: 10.1016/j.dsp.2013.10.019 CrossRefGoogle Scholar
  5. Ahirwal MK, Kumar A, Singh GK (2014b) Adaptive filtering of EEG/ERP through noise cancellers using an improved PSO algorithm. Swarm Evol Comput 14:76–91. doi: 10.1016/j.swevo.2013.10.001 CrossRefGoogle Scholar
  6. Bansal JC, Singh PK, Saraswat M et al (2011) Inertia weight strategies in particle swarm optimization. In: 2011 Third world congress on nature and biologically inspired computing (NaBIC), pp 633–640Google Scholar
  7. Bhandari AK, Kumar A, Singh GK (2015a) Improved knee transfer function and gamma correction based method for contrast and brightness enhancement of satellite image. AEU Int J Electron Commun 69:579–589. doi: 10.1016/j.aeue.2014.11.012 CrossRefGoogle Scholar
  8. Bhandari AK, Kumar A, Singh GK (2015b) Modified artificial bee colony based computationally efficient multilevel thresholding for satellite image segmentation using Kapur’s, Otsu and Tsallis functions. Expert Syst Appl 42:1573–1601. doi: 10.1016/j.eswa.2014.09.049 CrossRefGoogle Scholar
  9. Cao L, Zhang D, Tang S, Deng F (2016) A practical parameter determination strategy based on improved hybrid PSO algorithm for higher-order sliding mode control of air-breathing hypersonic vehicles. Aerosp Sci Technol 59:1–10. doi: 10.1016/j.ast.2016.10.001 CrossRefGoogle Scholar
  10. Etter DM, Hicks MJ, Cho KH (1982) Recursive adaptive filter design using an adaptive genetic algorithm, pp 635–638Google Scholar
  11. Gong D, Zhang Y, Qi C (2010) Environmental/economic power dispatch using a hybrid multi-objective optimization algorithm. Int J Electr Power Energy Syst 32:607–614. doi: 10.1016/j.ijepes.2009.11.017 CrossRefGoogle Scholar
  12. Hartmann A, Lemos JM, Costa RS, Vinga S (2014) Identifying IIR filter coefficients using particle swarm optimization with application to reconstruction of missing cardiovascular signals. Eng Appl Artif Intell 34:193–198. doi: 10.1016/j.engappai.2014.05.014 CrossRefGoogle Scholar
  13. Karaboga D (2010) Artificial bee colony algorithm. Scholarpedia 5:6915Google Scholar
  14. Karaboga D, Basturk B (2007a) Artificial bee colony (ABC) optimization algorithm for solving constrained optimization problems. Springer, BerlinCrossRefMATHGoogle Scholar
  15. Karaboga D, Basturk B (2007b) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471. doi: 10.1007/s10898-007-9149-x MathSciNetCrossRefMATHGoogle Scholar
  16. Karaboga N (2009) A new design method based on artificial bee colony algorithm for digital IIR filters. J Frankl Inst 346:328–348. doi: 10.1016/j.jfranklin.2008.11.003 MathSciNetCrossRefMATHGoogle Scholar
  17. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE international conference on neural networks, 1995, Proceedings, pp 1942–1948Google Scholar
  18. Kobayashi T, Imai S (1990) Complex Chebyshev approximation for IIR digital filters using an iterative WLS technique. In: International conference on acoustics, speech, and signal processing. IEEE, pp 1321–1324Google Scholar
  19. Krusienski DJ, Jenkins WK (2003) Adaptive filtering via particle swarm optimization. In: The thirty-seventh asilomar conference on signals, systems and computers, 2003, IEEE, pp 571–575Google Scholar
  20. Kuldeep B, Kumar A, Singh GK (2015a) Design of multi-channel filter bank using ABC optimized fractional derivative constraints. In: International conference on communication and signal processing, pp 492–496Google Scholar
  21. Kuldeep B, Singh VK, Kumar A, Singh GK (2015b) Design of two-channel filter bank using nature inspired optimization based fractional derivative constraints. ISA Trans 54:101–116. doi: 10.1016/j.isatra.2014.06.005 CrossRefGoogle Scholar
  22. Kumar A, Singh GK, Anand RS (2010) An improved method for designing quadrature mirror filter banks via unconstrained optimization. J Math Model Algorithms 9:99–111. doi: 10.1007/s10852-009-9122-4 MathSciNetCrossRefMATHGoogle Scholar
  23. Kumar A, Singh GK, Anand RS (2013) An improved method for the design of quadrature mirror filter banks using the Levenberg-Marquardt optimization. Signal Image Video Process 7:209–220. doi: 10.1007/s11760-011-0209-9 CrossRefGoogle Scholar
  24. Kumar R, Kumar A, Pandey RK (2012) Electrocardiogram signal compression using beta wavelets. J Math Model Algorithms 11:35–248. doi: 10.1007/s10852-012-9181-9 MathSciNetCrossRefMATHGoogle Scholar
  25. Lang MC (2000) Least-squares design of IIR filters with prescribed magnitude and phase responses and a pole radius constraint. Signal Process IEEE Trans 48:3109–3121. doi: 10.1109/78.875468 CrossRefGoogle Scholar
  26. Nongpiur RC, Shpak DJ, Antoniou A (2013) Improved design method for nearly linear-phase IIR filters using constrained optimization. IEEE Trans Signal Process 61:895–906. doi: 10.1109/TSP.2012.2231678 MathSciNetCrossRefGoogle Scholar
  27. Proakis JG, Manolakis DG (2006) Digital signal processing, 4th edn. Prentice Hall, Upper Saddle RiverGoogle Scholar
  28. Rafi SM, Kumar A, Singh GK (2013) An improved particle swarm optimization method for multirate filter bank design. J Frankl Inst 350:757–769MathSciNetCrossRefMATHGoogle Scholar
  29. Saha SK, Kar R, Mandal D, Ghoshal SP (2011) IIR filter design with craziness based particle swarm optimization technique. Inter J Elect Comp Ener Elect Comm Eng 5(12):1810–1817Google Scholar
  30. Saha S, Chaudhuri A, Mandal D et al (2012a) Optimization of IIR high pass filter using craziness based particle swarm optimization technique. In: 2012 IEEE symposium on humanities, science and engineering research (SHUSER), pp 401–406Google Scholar
  31. Saha SK, Kar R, Mandal D, Ghoshal SP (2012b) Digital stable IIR low pass filter optimization using PSO-CFIWA. In: 2012 1st International conference on recent advances in information technology (RAIT), pp 196–201Google Scholar
  32. Saha SK, Kar R, Mandal D, Ghoshal SP (2013) An efficient craziness based particle swarm optimization technique for optimal IIR filter design. Trans Comput Sci 8160:230–252CrossRefGoogle Scholar
  33. Saha SK, Kar R, Mandal D, Ghoshal SP (2014) Gravitation search algorithm: application to the optimal IIR filter design. J King Saud Univ Eng Sci 26:69–81. doi: 10.1016/j.jksues.2012.12.003 Google Scholar
  34. Shao P, Wu Z, Zhou X, Tran DC (2015) FIR digital filter design using improved particle swarm optimization based on refraction principle. Soft Comput. doi: 10.1007/s00500-015-1963-3 Google Scholar
  35. Sharma I, Kumar A, Singh GK (2016) Adjustable window based design of multiplier-less cosine modulated filter bank using swarm optimization algorithms. AEU Int J Electron Commun 70:85–94. doi: 10.1016/j.aeue.2015.10.008 CrossRefGoogle Scholar
  36. Sheng C, Bing LL (2010) Digital IIR filter design using particle swarm optimisation. Int J Model Identif Control 9:327–335Google Scholar
  37. Sidhu DS, Dhillon JS, Kaur D (2016) Hybrid heuristic search method for design of digital IIR filter with conflicting objectives. Soft Comput. doi: 10.1007/s00500-015-2023-8 MATHGoogle Scholar
  38. Tang K-S, Man K-F, Kwong S, Liu Z-F (1998) Design and optimization of IIR filter structure using hierarchical genetic algorithms. IEEE Trans Ind Electron 45:481–487. doi: 10.1109/41.679006 CrossRefGoogle Scholar
  39. Weidong G, Fan J (2003) Multi-criterion satisfactory optimization method for designing IIR digital filters. In: International conference on communication technology proceedings, vol 2, pp 1484–1490. doi: 10.1109/ICCT.2003.1209809
  40. Yu Y, Xinjie Y (2007) Cooperative coevolutionary genetic algorithm for digital IIR filter design. Ind Electron IEEE Trans 54:1311–1318. doi: 10.1109/TIE.2007.893063 CrossRefGoogle Scholar
  41. Zhang Y, Gong D, Geng N, Sun X (2014) Hybrid bare-bones PSO for dynamic economic dispatch with valve-point effects. Appl Soft Comput 18:248–260. doi: 10.1016/j.asoc.2014.01.035 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.PDPM Indian Institute of Information Technology, Design and Manufacturing JabalpurJabalpurIndia

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