Skip to main content

Digital IIR Filter Design with Fix-Point Representation Using Effective Evolutionary Local Search Enhanced Differential Evolution

  • 650 Accesses

Abstract

Previously, the parameters of digital IIR filters were encoded with floating-point representations. It is known that a fixed-point representation can effectively save computational resources and is more convenient for direct realization on hardware. Inherently, compared with floating-point representation, fixed-point representation may make the search space miss much useful gradient information and, therefore, raises new challenges. In this chapter, the universality of DE-based MA is improved by implementing more efficient evolutionary algorithms (EAs) as the local search techniques. The performance of the newly designed algorithm is experimentally verified in both function optimization tasks and digital IIR filter design problems.

Keywords

  • Local Search
  • Differential Evolution
  • Global Search
  • Memetic Algorithm
  • Covariance Matrix Adaptation Evolution Strategy

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-20071-2_5
  • Chapter length: 27 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   99.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-20071-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book
USD   119.99
Price excludes VAT (USA)
Fig. 5.1
Fig. 5.2
Fig. 5.3
Fig. 5.4

References

  1. Auger, A., Hansen, N.: Performance evaluation of an advanced local search evolutionary algorithm. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 1777–1784 (2005)

    Google Scholar 

  2. Auger, A., Hansen, N.: A restart CMA evolution strategy with increasing population size. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 1769–1776 (2005)

    Google Scholar 

  3. Brest, J., Greiner, S., Boskovic, B., Mernik, M., Zumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. Evol. Comput. 10(6), 646–657 (2006)

    CrossRef  Google Scholar 

  4. Caponio, A., Kononova, A.V., Neri, F.: Differential evolution with scale factor local search for large scale problems. In: Tenne, Y., Goh, C.-K. (eds.) Computational Intelligence in Expensive Optimization Problems. Studies in Evolutionary Learning and Optimization, vol. 2, pp. 297–323. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  5. Chen, C.T.: One-Dimensional Digital Signal Processing. Marcel Dekker, New York (1979)

    Google Scholar 

  6. Choo, H., Muhammad, K., Roy, K.: Complexity reduction of digital filters using shift inclusive differential coefficients. IEEE Trans. Signal Process. 52(6), 1760–1772 (2004)

    CrossRef  Google Scholar 

  7. Dai, C.H., Chen, W.R., Zhu, Y.F.: Seeker optimization algorithm for digital IIR filter design. IEEE Trans. Ind. Electron 57(5), 1710–1718 (2010)

    CrossRef  Google Scholar 

  8. Das, S., Suganthan, P.N.: Differential evolution: a survey of the state-of-the-art. IEEE Trans. Evol. Comput. 15(1), 4–31 (2011)

    CrossRef  Google Scholar 

  9. Debye, P.: Näherungsformeln für die Zylinderfunktionen für gro\(\beta \)e Werte des Arguments und unbeschränkt veränderliche Werte des Index. Mathematische Annalen 67(4), 535–558 (1909)

    MathSciNet  CrossRef  MATH  Google Scholar 

  10. Dong, W., Yao, X.: Covariance matrix repairing in Gaussian based EDAs. In: IEEE Congress on Evolutionary Computation (CEC07), pp. 415–422 (2007)

    Google Scholar 

  11. Dong, W., Yao, X.: Unified eigen analysis on multivariate Gaussian based estimation of distribution algorithms. Inf. Sci. 178(15), 3000–3023 (2008)

    MathSciNet  CrossRef  MATH  Google Scholar 

  12. Dong, W., Yao, X.: NichingEDA: utilizing the diversity inside a population of EDAs for continuous optimization. In: IEEE Congress on Evolutionary Computation, pp. 1260–1267 (2008)

    Google Scholar 

  13. Dong, W., Zhang, X., Jiang, Z., Sun, W., Xie, L., Hampapur, A.: Detect irregularly shaped spatio-temporal clusters for decision support. In: IEEE International Conference on Service Operations, Logistics, and Informatics, pp. 231–236 (2011)

    Google Scholar 

  14. Dong, W., Zhang, X., Li, L., Sun, C., Shi, L., Sun, W.: Detecting irregularly shaped significant spatial and spatio-temporal clusters. SIAM Data Mining, pp. 732–743 (2012)

    Google Scholar 

  15. Dong, W., Li, L., Zhou, C., Wang, Y., Li, M., Tian, C., Sun, W.: Discovery of generalized spatial association rules. In: IEEE International Conference on Service Operations, Logistics, and Informatics, pp. 60–65 (2012)

    Google Scholar 

  16. Dong, W., Fan, W., Shi, L., Zhou, C., Yan, X.: A general framework to encode heterogeneous information sources for contextual pattern mining. In: ACM International Conference on Information and Knowledge Management, pp. 65–74 (2012)

    Google Scholar 

  17. Dong, W., Chen, T., Tino, P., Yao, X.: Scaling up estimation of distribution algorithms for continuous optimization. IEEE Trans. Evol. Comput. 17(6), 797–822 (2013)

    CrossRef  MATH  Google Scholar 

  18. Elloumi, S., Fortemps, P.: A hybrid rank-based evolutionary algorithm applied to multi-mode resource-constrained project scheduling problem. Eur. J. Oper. Res. 205, 31–41 (2010)

    MathSciNet  CrossRef  MATH  Google Scholar 

  19. Etter, D.M., Hicks, M.J., Cho, K.H.: Recursive adaptive filter design using an adaptive genetic algorithm. In: Proceedings of IEEE International Conference on ASSP, pp. 635–638 (1982)

    Google Scholar 

  20. Florios, K., Mavrotas, G., Diakoulaki, D.: Solving multiobjective, multiconstraint knapsack problems using mathematical programming and evolutionary algorithms. Eur. J. Oper. Res. 203, 14–21 (2010)

    MathSciNet  CrossRef  MATH  Google Scholar 

  21. Garcia-Najera, A., Bullinaria, J.A.: An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows. Comput. Oper. Res. 38(1), 287–300 (2011)

    MathSciNet  CrossRef  MATH  Google Scholar 

  22. Hanne, T.: A multiobjective evolutionary algorithm for approximating the efficient set. Eur. J. Oper. Res. 176, 1723–1734 (2007)

    MathSciNet  CrossRef  MATH  Google Scholar 

  23. Hanne, T., Nickel, S.: A multiobjective evolutionary algorithm for scheduling and inspection planning in software development projects. Eur. J. Oper. Res. 167, 663–678 (2005)

    MathSciNet  CrossRef  MATH  Google Scholar 

  24. Harris, S.P., Ifeachor, E.C.: Automatic design of frequency sampling filters by hybrid genetic algorithm techniques. IEEE Trans. Signal Process. 46(12), 3304–3314 (1998)

    CrossRef  MATH  Google Scholar 

  25. Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evol. Comput. 9(2), 159–195 (2001)

    CrossRef  Google Scholar 

  26. Hasan, S., Sarker, R., Essam, D., Cornforth, D.: Memetic algorithms for solving job-shop scheduling problems. Memet. Comput. 1(1), 69–83 (2009)

    CrossRef  Google Scholar 

  27. Haseyama, M., Matsuura, D.: A filter coefficient quantization method with genetic algorithm, including simulated annealing. IEEE Signal Process. Lett. 13(4), 189–192 (2006)

    CrossRef  Google Scholar 

  28. Hestenes, R.M., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Natl Bur. Stand. 49(6), 409–436 (1952)

    MathSciNet  CrossRef  MATH  Google Scholar 

  29. Houck, C.: Joines, J., Kay, M.: Utilizing Lamarckian evolution and the Baldwin effect in hybrid genetic algorithms. NCSU-IE Technical Report 96-01, Meta-Heuristic Research and Applications Group, Department of Industrial Engineering, North Carolina State University (1996)

    Google Scholar 

  30. Kalinli, A., Karaboga, N.: Artificial immune algorithm for IIR filter design. J. Eng. Appl. Artif. Intell. 18(5), 919–929 (2005)

    CrossRef  Google Scholar 

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

    CrossRef  Google Scholar 

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

    CrossRef  MATH  Google Scholar 

  33. Kennedy, J., Mendes, R.: Population structure and particle swarm performance. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 1671–1676 (2002)

    Google Scholar 

  34. Kim, Y.K., Park, K., Ko, J.: A symbiotic evolutionary algorithm for the integration of process planning and job shop scheduling. Comput. Oper. Res. 30(8), 1151–1171 (2003)

    MathSciNet  CrossRef  MATH  Google Scholar 

  35. Krasnogor, N., Smith, J.: A tutorial for competent memetic algorithms: model, taxonomy, and design issues. IEEE Trans. Evol. Comput. 9(5), 474–488 (2005)

    CrossRef  Google Scholar 

  36. Krusienski, D.J., Jenkins, W.K.: Design and performance of adaptive systems based on structured stochastic optimization. IEEE Circuits Syst. Mag. 5(1), 8–20 (2005)

    CrossRef  Google Scholar 

  37. Liang, J.J., Suganthan, P.N.: Dynamic multi-swarm particle swarm optimizer with local search. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 522–528 (2005)

    Google Scholar 

  38. Liang, J.J., Qin, A.K., Suganthan, P.N., Baskar, S.: Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans. Evol. Comput. 10(3), 281–295 (2006)

    CrossRef  Google Scholar 

  39. Liao, T.W.: Two hybrid differential evolution algorithms for engineering design optimization. Appl. Soft Comput. 10(4), 1188–1199 (2010)

    CrossRef  Google Scholar 

  40. Lozano, M., García-Martínez, C.: Hybrid metaheuristics with evolutionary algorithms specializing in intensification and diversification: overview and progress report. Comput. Oper. Res. 37(3), 481–497 (2010)

    MathSciNet  CrossRef  MATH  Google Scholar 

  41. Lu, Y.L., Zhou, J.Z., Qin, H., Li, Y.H., Zhang, Y.C.: An adaptive hybrid differential evolution algorithm for dynamic economic dispatch with valve-point effects. Expert Syst. Appl. 37(7), 4842–4849 (2010)

    CrossRef  Google Scholar 

  42. Lu, Y.L., Zhou, J.Z., Qin, H., Li, Y.H., Zhang, Y.C.: An adaptive chaotic differential evolution for the short-term hydrothermal generation scheduling problem. Energy Convers. Manag. 51(7), 1481–1490 (2010)

    CrossRef  Google Scholar 

  43. Mendes, R., Kennedy, J., Neves, J.: The fully informed particle swarm: simpler, maybe better. IEEE Trans. Evol. Comput. 8(3), 204–210 (2004)

    CrossRef  Google Scholar 

  44. Molina, D., Herrera, F., Lozano, M.: Adaptive local search parameters for real-coded memetic algorithms. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 888–895 (2005)

    Google Scholar 

  45. Moscato, P. : Genetic algorithms and martial arts: towards memetic algorithms. Publication Report 790, Caltech Concurrent Computation Program (1989)

    Google Scholar 

  46. Neri, F., Tirronen, V.: Recent advances in differential evolution: a review and experimental analysis. Artif. Intell. Rev. 33(1), 61–106 (2010)

    CrossRef  Google Scholar 

  47. Neumann, F.: Expected runtimes of evolutionary algorithms for the Eulerian cycle problem. Comput. Oper. Res. 35(9), 2750–2759 (2008)

    MathSciNet  CrossRef  MATH  Google Scholar 

  48. Nguyen, Q.H., Ong, Y.S., Lim, M.H.: A probabilistic memetic framework. IEEE Trans. Evol. Comput. 13(3), 604–623 (2009)

    CrossRef  Google Scholar 

  49. Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, Berlin (2006)

    MATH  Google Scholar 

  50. Noman, N., Iba, H.: Accelerating differential evolution using an adaptive local search. IEEE Trans. Evol. Comput. 12(1), 107–125 (2008)

    CrossRef  Google Scholar 

  51. Ong, Y.S., Keane, A.J.: Meta-Lamarckian learning in memetic algorithms. IEEE Trans. Evol. Comput. 8(2), 99–110 (2004)

    CrossRef  Google Scholar 

  52. Ong, Y.S., Lim, M.H., Zhu, N., Wong, K.W.: Classification of adaptive memetic algorithms: a comparative study. IEEE Trans. Syst. Man Cybern. Part B 36(1), 141–152 (2006)

    CrossRef  Google Scholar 

  53. Ong, Y.S., Lim, M.H., Chen, X.S.: Research frontier: memetic computation—past, present & future. IEEE Comput. Intell. Mag. 5(2), 24–36 (2010)

    CrossRef  Google Scholar 

  54. Pan, S.T.: A canonic-signed-digit coded genetic algorithm for designing finite impulse response digital filter. Digit. Signal Process. 20(314–327), 2010 (2010)

    Google Scholar 

  55. Pena, J.M., Robles, V., Larranaga, P., Herves, V., Rosales, F., Perez, M.S.: GA-EDA: hybrid evolutionary algorithm using genetic and estimation of distribution algorithms. Proc. Lect. Notes Comput. Sci. 3029, 361–371 (2004)

    CrossRef  Google Scholar 

  56. Peram, T., Veeramachaneni, K., Mohan, C.K.: Fitness-distance-ratio based particle swarm optimization. In: Proceedings of Swarm Intelligence Symposium, p. 174 (2003)

    Google Scholar 

  57. Powell, M.J.D.: An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput. J. 7(4), 303–307 (1964)

    CrossRef  Google Scholar 

  58. Prodhon, C.: A hybrid evolutionary algorithm for the periodic location-routing problem. Eur. J. Oper. Res. 210, 204–212 (2011)

    MathSciNet  CrossRef  MATH  Google Scholar 

  59. Qin, A.K., Suganthan, P.N.: Self-adaptive differential evolution algorithm for numerical optimization. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 1785–1791 (2005)

    Google Scholar 

  60. Qin, A.K., Huang, V.L., Suganthan, P.N.: Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans. Evol. Comput. 13(2), 398–417 (2009)

    CrossRef  MATH  Google Scholar 

  61. Rökkönen, J., Kukkonen, S., Price, K.V.: Real-parameter optimization with differential evolution. In: Proceedings of IEEE Congress on Evolutionary Computation (CEC), pp. 506–513 (2005)

    Google Scholar 

  62. dos Santos Coelho, L., Cocco Mariani, V.: Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect. IEEE Trans. Power Syst. 21(2), 989–996 (2006)

    CrossRef  Google Scholar 

  63. Shah, R., Reed, P.: Comparative analysis of multiobjective evolutionary algorithms for random and correlated instances of multiobjective d-dimensional knapsack problems. Eur. J. Oper. Res. 211, 466–479 (2011)

    MathSciNet  CrossRef  Google Scholar 

  64. Shynk, J.J.: Adaptive IIR filtering. IEEE ASSP Mag. 6(2), 4–21 (1989)

    CrossRef  Google Scholar 

  65. Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic strategy for global optimization over continuous spaces. J. Glob. Optim. 11, 341–359 (1997)

    MathSciNet  CrossRef  MATH  Google Scholar 

  66. Sun, J., Zhang, Q.F., Tsang, E.: DE/EDA: a new evolutionary algorithm for global optimization. Inf. Sci. 169, 249–262 (2005)

    MathSciNet  CrossRef  Google Scholar 

  67. Tan, K.C., Chew, Y.H., Lee, L.H.: A hybrid multi-objective evolutionary algorithm for solving truck and trailer vehicle routing problems. Eur. J. Oper. Res. 172, 855–885 (2006)

    MathSciNet  CrossRef  MATH  Google Scholar 

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

    CrossRef  Google Scholar 

  69. Tarczynski, A., Cain, G.D., Hermanowicz, E., Rojewski, M.: A WISE method for designing IIR filters. IEEE Trans. Signal Process. 49(7), 1421–1432 (2001)

    MathSciNet  CrossRef  Google Scholar 

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

    CrossRef  Google Scholar 

  71. Vanuytsel, G., Boets, P., Van Biesen, L., Temmerman, S.: Efficient hybrid optimization of fixed-point cascaded IIR filter coefficients. In: Proceedings of IEEE Instrumentation and Measurement, pp. 793–797 (2002)

    Google Scholar 

  72. Vicini, A., Quagliarella, D.: Airfoil and wing design using hybrid optimization strategies. Am. Inst. Aeronaut. Astronaut. J. 37(5), 634–641 (1999)

    CrossRef  Google Scholar 

  73. Vrugt, J.A., Robinson, B.A., Hyman, J.M.: Self-adaptive multimethod search for global optimization in real-parameter spaces. IEEE Trans. Evol. Comput. 13(2), 243–259 (2009)

    CrossRef  Google Scholar 

  74. Wang, R., Dong, W., Wang, Y., Tang, K., Yao, X.: Pipe failure prediction: a data mining method. In: IEEE International Conference on Data Engineering, pp. 1208–1218 (2013)

    Google Scholar 

  75. Wang, Y., Li, B.: A restart univariate estimation of distribution algorithm: sampling under mixed Gaussian and Levy probability distribution. In: Proceedings of IEEE Congress on Evolutionary Computation (CEC 2008), pp. 3218–3925 (2008)

    Google Scholar 

  76. Wang, Y., Li, B.: A self-adaptive mixed distribution based uni-variate estimation of distribution algorithm for large scale global optimization. In: Chiong, R. (ed.) Nature-Inspired Algorithms for Optimization. Studies in Computational Intelligence, pp. 171–198. Springer, New York (2009)

    CrossRef  Google Scholar 

  77. Wang, Y., Li, B., Weise, T.: Estimation of distribution and differential evolution cooperation for large scale economic load dispatch optimization of power systems. Inf. Sci. 180(12), 2405–2420 (2011)

    CrossRef  Google Scholar 

  78. Wang, Y., Li, B.: Two-stage based ensemble optimization for large-scale global optimization. In: Proceedings of IEEE Congress on Evolutionary Computation (CEC 2010), pp. 1–8 (2011)

    Google Scholar 

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

    MathSciNet  CrossRef  Google Scholar 

  80. Wang, Y., Li, B., Weise, T., Wang, J.Y., Yuan, B., Tian, Q.J.: Self-adaptive learning based particle swarm optimization. Inf. Sci. 181(20), 4515–4538 (2011)

    CrossRef  MATH  Google Scholar 

  81. Wang, Y., Li, B., Zhang, K.B.: Estimation of distribution and differential evolution cooperation for real-world numerical optimization problems. In: Proceedings of IEEE Congress on Evolutionary Computation (CEC 2011), pp. 1315–1321 (2011)

    Google Scholar 

  82. Wang, Y., Li, B., Weise, T.: Two-Stage ensemble memetic algorithm: function optimization and digital IIR filter design. Inf. Sci. 220(20), 408–424 (2013)

    CrossRef  Google Scholar 

  83. Wang, Y., Huang, J., Dong, W., Yan, J., Tian, C., Li, M., Mo, W.: Two-stage based ensemble optimization framework for large-scale global optimization. Eur. J. Oper. Res. 228(2), 308–320 (2013)

    MathSciNet  CrossRef  Google Scholar 

  84. Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1), 67–82 (1997)

    CrossRef  Google Scholar 

  85. Yan, J., Li, Y., Zheng, E., Liu, Y.: An accelerated human motion tracking system based on voxel reconstruction under complex environments. In: Asian Conference on Computer Vision (ACCV), pp. 313–324 (2009)

    Google Scholar 

  86. Yan, J., Zhu, M., Liu, H., Liu, Y.: Visual saliency detection via sparsity pursuit. IEEE Signal Process. Lett. 17(8), 739–742 (2010)

    CrossRef  Google Scholar 

  87. Yan, J., Shen, S., Li, Y., Liu, Y.: An optimization based framework for human pose estimation. IEEE Signal Process. Lett. 17(8), 766–769 (2010)

    CrossRef  Google Scholar 

  88. Yan, J., Zhu, M., Liu, H., Liu, Y.: Visual saliency detection via rank-sparsity decomposition. In: 2010 17th IEEE International Conference on Image Processing (ICIP), pp. 1089–1092 (2010)

    Google Scholar 

  89. Yan, J., Song, J., Wang, L., Liu, Y.: Model-based 3D human motion tracking and voxel reconstruction from sparse views. In: 2010 17th IEEE International Conference on Image Processing (ICIP), pp. 3265–3268 (2010)

    Google Scholar 

  90. Yan, J., Tong, M.: Weighted sparse coding residual minimization for visual tracking. In: 2011 IEEE Visual Communications and Image Processing (VCIP), pp. 1–4 (2011)

    Google Scholar 

  91. Yan, J., Tian, C., Huang, J., Albertao, F.: Incremental dictionary learning for fault detection with applications to oil pipeline leakage detection. Electron. Lett., IET 47(21), 1198–1199 (2011)

    CrossRef  Google Scholar 

  92. Yan, J., Wang, Y., Zhou, K., Huang, J., Tian, C., Zha, H.: Towards effective prioritizing water pipe replacement and rehabilitation. In: Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence, pp. 2931–2937. AAAI Press (2013)

    Google Scholar 

  93. Yao, X., Liu, Y.: Evolutionary programming made faster. IEEE Trans. Evol. Comput. 3(2), 82–102 (1999)

    CrossRef  Google Scholar 

  94. Yu, Y., Yu, X.J.: Cooperative coevolutionary genetic algorithm for digital IIR filter design. IEEE Trans. Ind. Electron 54(3), 1811–1819 (2007)

    CrossRef  Google Scholar 

  95. Zhang, C., Ruan, X., Zhao, Y.M., Yang, M.H.: Contour detection via random forest. Proc. Int. Conf. Pattern Recogn. 2012, 2772–2775 (2012)

    Google Scholar 

  96. Zhang, C., Li, X., Ruan, X., Zhao, Y.M., Yang, M.H.: Discriminative generative contour detection. In: Proceedings of the British Machine Vision Conference 2013, pp. 74.1–74.11 (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yu Wang .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Wang, Y. et al. (2015). Digital IIR Filter Design with Fix-Point Representation Using Effective Evolutionary Local Search Enhanced Differential Evolution. In: Fakhfakh, M., Tlelo-Cuautle, E., Siarry, P. (eds) Computational Intelligence in Digital and Network Designs and Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-20071-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-20071-2_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20070-5

  • Online ISBN: 978-3-319-20071-2

  • eBook Packages: Computer ScienceComputer Science (R0)