Genetic algorithm for the design of optimal iir digital filters
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This document presents a method for designing digital IIR filters with arbitrary magnitude responses using a modified genetic algorithm. A genetic algorithm that operates on a continuous search space is developed and optimized with new genetic operators. A filter design algorithm is also developed to handle the specific requirements of the filter design problem, such as mapping filters to the genetic algorithm, evaluating fitness, creating initial populations, and ensuring realizability.
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References:
[1] S. Mitra, Digital Signal Processing: A Computer-Based Approach, 2nd ed. Boston: McGraw-Hill Irwin,
2001.
[2] R. Mersereau & M. Smith, Digital Filtering: A Computer Laboratory Textbook. John Wiley & Sons, Inc,
1994.
[3] D. Goldberg, Genetic Algorithm in Search, Optimization, and Machine Learning. Reading, MA:
Addison Wesley Pub. Co., 1989.
[4] J. Holland, Adaptation in Natural and Arti¯cial Systems. Ann Arbor, MI: The Univeristy of Michigan
Press, 1975.
[5] C. Darwin, The Origin of Species, ser. The Harvard Classics. New York: P F Collier & Son, 1909, vol. 11.
[6] W. Edmonson et al., A global least mean square algorithm for adaptive iir ¯ltering," IEEE Trans. on
Circuits and Systems, vol. 45, no. 3, pp. 379-384, Mar 1998.
[7] D. Talla, S. Rao, & L. John, An evolutionary computation embedded iir lms algorithm," in Proceedings
of International Conference on Signal Processing Applications and Technology, Orlando, FL, Nov 1-4,
1999.
[8] L. Wang, W. Li, & D. Zheng, A class of hybrid strategy for adaptive iir filter design." Shanghai, China:
8th International Conference on Neuaral Information Processing, Nov 14-18, 2001.
[9] A. Ko·sir & J. Tasi·c, Genetic algorithm and ¯ltering." She±eld, UK: First International Conference on
Genetic Algorithms in Engineering Systems: Innovations and Applications, Sep 14-18, 1995.
[10] D. Dumitrescu et al., Evolutionary Computation. Boca Raton, FL: CRC Press, 2000.
[11] L. Davis & M. Steenstrup, Genetic algorithms and simulated annealing: An overview," in Genetic
Algorithms and Simulated Annealing, L. Davis, Ed. London: Morgan Kaufmann Pub., 1987, pp. 1{11.
[12] L. Booker, Improving search in genetic algorithms," in Genetic Algorithms and Simulated Annealing,
L. Davis, Ed. London: Morgan Kaufmann Pub., 1987, pp. 61-73.
[13] J. Grefenstette, Rank-based selection," in Evolutionary Computation I: Basic Algorithms and
Operators, T. BÄack, D. Fogel, and Z. Michalewicz, Ed. Bristol, UK: Institute of Physics Publishing, 2000,
vol. 1, pp. 187{194.
[14] H. MÄuhlenbein & D. Schlierkamp-Voosen, The science of breeding and its application to the
breeder genetic algorithm (bga)," in Evolutionary Computation, vol. 1. Cambridge, MA: MIT Press, 1993,
pp. 335-360.
[15] ||, Predictive models for the breeder genetic algorithm: I. continuous parameter optimization," in
Evolutionary Computation, vol. 1. Cambridge, MA: MIT Press, 1993, pp. 25{50.
[16] G. Syswerda, Uniform crossover in genetic algorithms," in Proceedings of the Third International
Conference on Genetic Algorithms, D. Scha®er, Ed. George Mason University: Morgan Kaufmann Pub.,
Jun 1989, pp. 2-9.](https://image.slidesharecdn.com/geneticalgorithmforthedesignofoptimaliirdigitalfilters-130830121027-phpapp01/85/Genetic-algorithm-for-the-design-of-optimal-iir-digital-filters-8-320.jpg)
![Base paper: - http://www.scirp.org/journal/PaperDownload.aspx?paperID=22105
[17] T. BÄack & D. Fogel, Mutation operators," in Evolutionary Computation I: Basic Algorithms and
Operators, T. BÄack, D. Fogel, and Z. Michalewicz, Ed. Bristol, UK: Institute of Physics Publishing, 2000,
vol. 1.
[18] R. Craighurst & W. Martin, Enhancing ga performance through crossover prohibition based on
ancestory," in Proceedings of the Sixth International Conference on Genetic Algorithms, L. Eshelman, Ed.
University of Pittsburgh: Morgan Kaufmann Pub., Jul 1995, pp. 130{135.
[19] L. Eshelman & D. Scha®er, Preventing premature convergence in genetic algorithms by preventing
incest," in Proceedings of the Fourth International Conference on Genetic Algorithms, R. Belew & L.
Booker, Ed. University of California, San Diego: Morgan Kaufmann Pub., Jul 1991, pp. 115-122.
[20] D. Scha®er & L. Eshelman, On crossover as an evolutionary viable strategy," in Proceedings of the
Fourth International Conference on Genetic Algorithms, R. Belew & L. Booker, Ed. University of
California, San Diego: Morgan Kaufmann Pub., Jul 1991, pp. 61{68.
[21] D. Goldberg, Simple genetic algorithms and the minimal, deceptive problem," in Genetic
Algorithms and Simulated Annealing, L. Davis, Ed. London: Morgan Kaufmann Pub., 1987, pp. 74{88.
[22] J. Antonisse, A new interpretation of schema notation that overturns the binary encoding
constraint," in Proceedings of the Third International Conference on Genetic Algorithms, D. Scha®er, Ed.
George Mason University: Morgan Kaufmann Pub., Jun 1989, pp. 86{91.
[23] C. Janikow & Z. Michalewicz, An experimental comparison of binary and °oating point
representations in genetic algorithms," in Proceedings of the Fourth International Conference on Genetic
Algorithms, R. Belew & L. Booker, Ed. University of California, San Diego: Morgan Kaufmann Pub., Jul
1991, pp. 31-36.
[24] Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs. Berlin: Springer-Verlag,
1992.
[25] K. D. Jong, Analysis of the behavior of a class of genetic adaptive systems," Ph.D. dissertation,
University of Michigan, Ann Arbor, MI, 1975.
[26] W. Spears, The role of mutation and recombination in evolutionary algorithms," Ph.D. dissertation,
George Mason University, Fairfax, VA, 1998.
[27] A. Williams & F. Taylor, Electronic Filter Design Handbook, 3rd ed. New York: McGraw-Hill, Inc,
1995.](https://image.slidesharecdn.com/geneticalgorithmforthedesignofoptimaliirdigitalfilters-130830121027-phpapp01/85/Genetic-algorithm-for-the-design-of-optimal-iir-digital-filters-9-320.jpg)
Genetic algorithm for the design of optimal iir digital filters
- 1. Base paper: - http://www.scirp.org/journal/PaperDownload.aspx?paperID=22105 Genetic Algorithm for the Design of Optimal IIR Digital Filters Journal of Signal and Information Processing Abstract: A method for designing a digital IIR filter with arbitrary magnitude response using a modified genetic algorithm (GA) is presented. A GA that operates on a complex, continuous search space is constructed and optimized by statistically determining the abilities of commonly used genetic operators. Furthermore, a new genetic operator is presented; it combines crossover and adaptive mutation to improve the convergence rate and solution quality of the GA. A customized application layer, called the Filter Design Algorithm (FDA), has been developed for the optimized GA to handle the specific format and properties of the filter design problem. These requirements include a method for mapping a filter into the GA, evaluating the fitness of a filter, creating an initial population of filters, and ensuring that all filters are realizable.
- 2. Base paper: - http://www.scirp.org/journal/PaperDownload.aspx?paperID=22105 (a) Traditional Discrete Generic Algorithm (DGA) Block Diagram
- 3. Base paper: - http://www.scirp.org/journal/PaperDownload.aspx?paperID=22105 (b) Block Diagram of Continuous Generic Algorithm (CGA)
- 4. Base paper: - http://www.scirp.org/journal/PaperDownload.aspx?paperID=22105 FDA_RUN.m This file contains functions for Generic algorithm which is implemented by FDA_ANALYZE to design filters. FDA_ANALYZE Designs
- 5. Base paper: - http://www.scirp.org/journal/PaperDownload.aspx?paperID=22105
- 6. Base paper: - http://www.scirp.org/journal/PaperDownload.aspx?paperID=22105
- 7. Base paper: - http://www.scirp.org/journal/PaperDownload.aspx?paperID=22105 Note that minimum fitness and all diagrams may change during each run. Population generated can be different during each run.
- 8. Base paper: - http://www.scirp.org/journal/PaperDownload.aspx?paperID=22105 References: [1] S. Mitra, Digital Signal Processing: A Computer-Based Approach, 2nd ed. Boston: McGraw-Hill Irwin, 2001. [2] R. Mersereau & M. Smith, Digital Filtering: A Computer Laboratory Textbook. John Wiley & Sons, Inc, 1994. [3] D. Goldberg, Genetic Algorithm in Search, Optimization, and Machine Learning. Reading, MA: Addison Wesley Pub. Co., 1989. [4] J. Holland, Adaptation in Natural and Arti¯cial Systems. Ann Arbor, MI: The Univeristy of Michigan Press, 1975. [5] C. Darwin, The Origin of Species, ser. The Harvard Classics. New York: P F Collier & Son, 1909, vol. 11. [6] W. Edmonson et al., A global least mean square algorithm for adaptive iir ¯ltering," IEEE Trans. on Circuits and Systems, vol. 45, no. 3, pp. 379-384, Mar 1998. [7] D. Talla, S. Rao, & L. John, An evolutionary computation embedded iir lms algorithm," in Proceedings of International Conference on Signal Processing Applications and Technology, Orlando, FL, Nov 1-4, 1999. [8] L. Wang, W. Li, & D. Zheng, A class of hybrid strategy for adaptive iir filter design." Shanghai, China: 8th International Conference on Neuaral Information Processing, Nov 14-18, 2001. [9] A. Ko·sir & J. Tasi·c, Genetic algorithm and ¯ltering." She±eld, UK: First International Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications, Sep 14-18, 1995. [10] D. Dumitrescu et al., Evolutionary Computation. Boca Raton, FL: CRC Press, 2000. [11] L. Davis & M. Steenstrup, Genetic algorithms and simulated annealing: An overview," in Genetic Algorithms and Simulated Annealing, L. Davis, Ed. London: Morgan Kaufmann Pub., 1987, pp. 1{11. [12] L. Booker, Improving search in genetic algorithms," in Genetic Algorithms and Simulated Annealing, L. Davis, Ed. London: Morgan Kaufmann Pub., 1987, pp. 61-73. [13] J. Grefenstette, Rank-based selection," in Evolutionary Computation I: Basic Algorithms and Operators, T. BÄack, D. Fogel, and Z. Michalewicz, Ed. Bristol, UK: Institute of Physics Publishing, 2000, vol. 1, pp. 187{194. [14] H. MÄuhlenbein & D. Schlierkamp-Voosen, The science of breeding and its application to the breeder genetic algorithm (bga)," in Evolutionary Computation, vol. 1. Cambridge, MA: MIT Press, 1993, pp. 335-360. [15] ||, Predictive models for the breeder genetic algorithm: I. continuous parameter optimization," in Evolutionary Computation, vol. 1. Cambridge, MA: MIT Press, 1993, pp. 25{50. [16] G. Syswerda, Uniform crossover in genetic algorithms," in Proceedings of the Third International Conference on Genetic Algorithms, D. Scha®er, Ed. George Mason University: Morgan Kaufmann Pub., Jun 1989, pp. 2-9.
- 9. Base paper: - http://www.scirp.org/journal/PaperDownload.aspx?paperID=22105 [17] T. BÄack & D. Fogel, Mutation operators," in Evolutionary Computation I: Basic Algorithms and Operators, T. BÄack, D. Fogel, and Z. Michalewicz, Ed. Bristol, UK: Institute of Physics Publishing, 2000, vol. 1. [18] R. Craighurst & W. Martin, Enhancing ga performance through crossover prohibition based on ancestory," in Proceedings of the Sixth International Conference on Genetic Algorithms, L. Eshelman, Ed. University of Pittsburgh: Morgan Kaufmann Pub., Jul 1995, pp. 130{135. [19] L. Eshelman & D. Scha®er, Preventing premature convergence in genetic algorithms by preventing incest," in Proceedings of the Fourth International Conference on Genetic Algorithms, R. Belew & L. Booker, Ed. University of California, San Diego: Morgan Kaufmann Pub., Jul 1991, pp. 115-122. [20] D. Scha®er & L. Eshelman, On crossover as an evolutionary viable strategy," in Proceedings of the Fourth International Conference on Genetic Algorithms, R. Belew & L. Booker, Ed. University of California, San Diego: Morgan Kaufmann Pub., Jul 1991, pp. 61{68. [21] D. Goldberg, Simple genetic algorithms and the minimal, deceptive problem," in Genetic Algorithms and Simulated Annealing, L. Davis, Ed. London: Morgan Kaufmann Pub., 1987, pp. 74{88. [22] J. Antonisse, A new interpretation of schema notation that overturns the binary encoding constraint," in Proceedings of the Third International Conference on Genetic Algorithms, D. Scha®er, Ed. George Mason University: Morgan Kaufmann Pub., Jun 1989, pp. 86{91. [23] C. Janikow & Z. Michalewicz, An experimental comparison of binary and °oating point representations in genetic algorithms," in Proceedings of the Fourth International Conference on Genetic Algorithms, R. Belew & L. Booker, Ed. University of California, San Diego: Morgan Kaufmann Pub., Jul 1991, pp. 31-36. [24] Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs. Berlin: Springer-Verlag, 1992. [25] K. D. Jong, Analysis of the behavior of a class of genetic adaptive systems," Ph.D. dissertation, University of Michigan, Ann Arbor, MI, 1975. [26] W. Spears, The role of mutation and recombination in evolutionary algorithms," Ph.D. dissertation, George Mason University, Fairfax, VA, 1998. [27] A. Williams & F. Taylor, Electronic Filter Design Handbook, 3rd ed. New York: McGraw-Hill, Inc, 1995.