Share This Article:

Genetic Algorithm for the Design of Optimal IIR Digital Filters

Abstract Full-Text HTML Download Download as PDF (Size:426KB) PP. 286-292
DOI: 10.4236/jsip.2012.33038    7,235 Downloads   12,197 Views   Citations

ABSTRACT

This paper presents the design of Optimal Infinite-Impulse Response (IIR) digital filters using Genetic Algorithm (GA). IIR filter is essentially a digital filter with Recursive responses. Since the error surface of digital IIR filters is generally nonlinear and multimodal, global optimization techniques are required in order to avoid local minima. This paper presents heuristic way for the designing IIR filters. GA is a powerful global optimization algorithm introduced in combinatorial optimization problems. The paper finds the optimum Coefficients of IIR digital filter through GA. Design of Lowpass and High pass IIR digital filter is proposed to provide estimate of transition band. It is found that the calculated values are more optimal than fda tool available for the design of filter in MATLAB. The simulation result of the employed examples shows an improvement on transition band and mean-square-error (MSE). The position of pole-zero is also presented to describe stability and results are compared with Simulated Annealing (SA) method.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

R. Singh and S. Arya, "Genetic Algorithm for the Design of Optimal IIR Digital Filters," Journal of Signal and Information Processing, Vol. 3 No. 3, 2012, pp. 286-292. doi: 10.4236/jsip.2012.33038.

References

[1] V. K. Ingle and J. G. Proakis, “Digital Signal Processing Using MATLAB,” Thomson Books, New Delhi, 2004.
[2] J. G. Proakis and D. G. Manolakis, “Digital Signal Processing: Principles, Algorithms, and Applications,” 4th Edition, Pearson Education, Inc., New Delhi, 2007.
[3] P. Tarasewich and P. R. McMullen, “Swarm Intelli- gence,” Communication of the ACM, Vol. 45, No. 8, 2002, pp. 62-67.
[4] L. Y. Cao, “Practical Issues in Implementing a Single- Pole Low-Pass IIR Filter,” IEEE Signal Processing Ma- gazine, November 2010, pp. 114-117.
[5] J. Skaf and P. B. Stephen, “Filter Design with Low Complexity Coefficients,” IEEE Transactions on Signal processing, Vol. 56, No. 7, 2008, pp. 3162-3170. doi:10.1109/TSP.2008.919386
[6] R. J. Vaccaro and B. F. Harrison, “Optimal Matrix-Filter Design,” IEEE Transactions on Signal processing, Vol. 44, No. 3, 1996, pp. 705-710. doi:10.1109/78.489044
[7] X. Zhang and H. Iwakura, “Design of IIR Digital Filters based on Eigen Value Problem,” IEEE Transactions on Signal processing, Vol. 44, No. 6, 1996, pp. 1325-1319. doi:10.1109/78.506600
[8] F. Argenti and E. Del Re, “Design of IIR Eigen Filters in the Frequency Domain,” IEEE Transactions on Signal processing, Vol. 46, No. 6, 1998, pp. 1694-1700. doi:10.1109/78.678495
[9] X. Yao, Y. Liu and G. M. Lin, “Evolutionary Program- ming Made Faster,” IEEE Transactions on Evolutionary Computation, Vol. 3, No. 2, 1999, pp. 83-102.
[10] N. Benvenuto and M. Marchesi, “Applications of Simulated Annealing for the Design of Digital Filters,” IEEE Transactions on Signal Processing, Vol. 40, No. 2, 1992, pp. 323-331. doi:10.1109/78.124942
[11] K. S. Tang, K. F. Man and S. Kwong, “Design and Optimization of Digital Filter Structure Using Genetic Algorithm,” IEEE Transactions on Industrial Electronics, Vol. 45, No. 3, 1998, pp. 481-489. doi:10.1109/41.679006
[12] K. D. Abdesselam, “Design of Stable, Causal, Perfect Reconstruction, IIR Uniform DFT Filters,” IEEE Transactions on Signal Processing, Vol. 48, No. 4, 2000, pp. 1110-1117. doi:10.1109/78.827544
[13] C. C. Tseng and S. C. Pei, “Stable IIR Notch Filter Design with Optimal Pole Placement,” IEEE Transactions on Signal Processing, Vol. 49, No. 11, 2001, pp. 2673- 2681. doi:10.1109/78.960414
[14] L. Liang, M. Ahmadi, M. Ahmed and K. Wallus, “Design of Canonical Signed Digital Filters Using Genetic Algorithms,” IEEE Transaction on Signal Processing, Vol. 3, No. 1, 2003, pp. 2043-2047.
[15] S. U. Ahmad and A. Antoniou, “Design of Digital Filters Using Genetic Algorithms,” IEEE Transaction on Signal Processing, Vol.1, No. 1, 2006, pp. 1-9.
[16] J. E. Cousseau, S. Werner and P. D. Donate, “Factorized All-Pass Based IIR Adaptive Notch Filters,” IEEE Tran- sactions on Signal Processing, Vol. 55, No. 11, 2007, pp. 5225-5236.
[17] B. W. Jung, H. J. Yang and J. Chun, “Finite Word length Digital Filter Design Using Simulated Annealing,” IEEE Transactions on Signal Processing, Vol. 15, No. 5, 2008, pp. 546- 550.
[18] C. H. Dai, W. R. Chen and Y. F. Zhu, “Seeker Optimization Algorithm for Digital IIR Filter Design,” IEEE Transaction on Evolutionary Computation, Vol. 57, No. 5, 2010, pp. 1710-1718.
[19] D. E. Goldberg, “Genetic Algorithm in Search, Optimiza- tion and Machine Learning, Pearson Education,” Low Price Edition, Delhi, 2005.
[20] W. X. Zheng, “Adaptive Filter Design Subject to Output Envelop Constraints and Bounded Input Noise,” IEEE Transaction on Circuit & Systems-II Analog & Digital Signal Processing, Vol. 50, No. 12, 2003, pp. 1023-1027.
[21] Y. R. Zhou and J. He, “A Runtime Analysis of Evolutionary Algorithms for Constrained Optimization Problems,” IEEE Transactions on Evolutionary Computation, Vol. 11, No. 5, 2007, pp. 608-620. doi:10.1109/TEVC.2006.888929
[22] N. Benvenuto, M. Marchesi and A. Uncini, “Applications of Simulate Annealing for Design of Digital Filter,” IEEE Transactions on Signal Processing, Vol. 40, No. 2, 1992, pp. 323-332. doi:10.1109/78.124942
[23] J. Skaf and P. Boyd Stephen, “Filter Design with Low Complexity Coefficients,” IEEE Transactions on Signal Processing, Vol. 56, No. 7, 2008, pp. 3162-3170. doi:10.1109/TSP.2008.919386
[24] T. Weise and K. Tang, “Evolving Distributed Algorithms with Genetic Programming” IEEE Transactions on Evo- lutionary Computation, 2011, pp. 1-24.
[25] A. Antoniou, “Digital Filters Analysis, Design and Application,” Tata Mcgraw-Hill Edition, New Delhi, 2005.
[26] R. S. Chauhan and S. K. Arya, “An Optimal Design of FIR Digital Filter Using Genetic Algorithm,” Lecture Notes in Computer Science (LNCS) Springer-Verlag Berlin Heidelberg, Vol. 168, No. 1, 2011, pp. 51-56.
[27] H. Ali, A. Doucet and D. I. Amshah, “GSR: A New Genetic Algorithm for Improving Source and Channel Estimates,” IEEE Transactions on Circuits and Systems-I, Vol. 54, No. 5, 2007, pp. 1088-1098. doi:10.1109/TCSI.2007.893507

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.