Abstract
Evolutionary algorithms possesses many practical applications. One of the practical application of the evolutionary methods is digital filters design. Evolutionary techniques are very often used to design FIR (Finite Impulse Response) digital filters or IIR (Infinite Impulse Response) digital filters. IIR digital filters are very often practically realized as a cascade of biquad sections. The guarantee of stability of biquad sections is one of the most important element during IIR digital filter design process. If we want to obtain a stable IIR digital filter, the all poles of the transfer function for all biquad sections must be located into the unitary circle in the z-plane. Of course, if we want to have a minimal phase digital filter then all zeros of the transfer function for all biquad sections must be also located into the unitary circle in the z-plane. In many evolutionary algorithms which are dedicated to the IIR digital filter design the initial population (or re-initialized populations) of the filter coefficients are chosen randomly. Therefore, some of digital filters which are generated in population can be unstable (or/and the filters are not minimal phase). In this paper, we show how to randomly generate a population of stable and minimal phase biquad sections with very high efficiency. Due to our approach, we can also reduce a computational time which is required for evaluation of stability (or/and minimal phase property) of digital filter. The proposed approach has been compared with standard techniques which are used in evolutionary digital filter design methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Publishing Company Inc., Boston (1989)
Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, Berlin (1992)
Vasicek, Z., Sekanina, L.: Evolutionary approach to approximate digital circuits design. IEEE Trans. Evol. Comput. 19(3), 432–444 (2015)
Preen, R.J., Bull, L.: Toward the coevolution of novel vertical-axis wind turbines. IEEE Trans. Evol. Comput. 19(2), 284–294 (2015)
Tersi, L., Fantozzi, S., Stagni, R.: Characterization of the performance of memetic algorithms for the automation of bone tracking with fluoroscopy. IEEE Trans. Evol. Comput. 19(1), 19–30 (2015)
Graditi, G., Di Silvestre, M.L., Gallea, R., Riva Sanseverino, E.: Heuristic-based shiftable loads optimal management in smart micro-grids. IEEE Trans. Ind. Inform. 11(1), 271–280 (2015)
Kim, J., Lee, J.: Trajectory optimization with particle swarm optimization for manipulator motion planning. IEEE Trans. Ind. Inform. 11(3), 620–631 (2015)
Aghaei, J., Baharvandi, A., Rabiee, A., Akbari, M.A.: Probabilistic PMU placement in electric power networks: an MILP-based multiobjective model. IEEE Trans. Ind. Inform. 11(2), 332–341 (2015)
Price, K.: An introduction to differential evolution. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization. McGraw-Hill, London (1999)
Kennedy, J., Eberhart, R.C., Shi, Y.: Swarm Intelligence. Morgan Kaufmann Publishers, San Francisco (2001)
Socha, K., Doringo, M.: Ant colony optimization for continuous domains. Eur. J. Oper. Res. 185(3), 1155–1173 (2008)
Erba, M., Rossi, R., Liberali, V., Tettamanzi, A.G.: Digital filter design through simulated evolution. In: Proceedings of ECCTD 2001, vol. 2, pp. 137–140 (2001)
Karaboga, N.: Digital IIR filter design using differential evolution algorithm. EURASIP J. Appl. Sig. Process. 2005(8), 1269–1276 (2005)
Benvenuto, N., Marchesi, M., Orlandi, G., Piazza, F., Uncini, A.: Finite wordlength digital filter design using an annealing algorithm. In: International Conference on Acoustics, Speech, and Signal Processing, vol. 2, pp. 861–864 (1989)
Nakamoto, M., Yoshiya, T., Hinamoto, T.: Finite word length design for IIR digital filters based on the modified least-square criterion in the frequency domain. In: International Symposium on Intelligent Signal Processing and Communication Systems, ISPACS, pp. 462–465 (2007)
Slowik, A., Bialko, M.: Design of IIR digital filters with non-standard characteristics using differential evolution algorithm. Bull. Pol. Acad. Sci. Tech. Sci. 55(4), 359–363 (2007)
Slowik, A., Bialko, M.: Design and optimization of IIR digital filters with non-standard characteristics using continuous ant colony optimization algorithm. In: Darzentas, J., Vouros, G.A., Vosinakis, S., Arnellos, A. (eds.) SETN 2008. LNCS (LNAI), vol. 5138, pp. 395–400. Springer, Heidelberg (2008). doi:10.1007/978-3-540-87881-0_39
Slowik, A.: Application of evolutionary algorithm to design of minimal phase digital filters with non-standard amplitude characteristics and finite bits word length. Bull. Pol. Acad. Sci. Tech. Sci. 59(2), 125–135 (2011). doi:10.2478/v10175-011-0016-z
Slowik, A.: Hybridization of evolutionary algorithm with Yule Walker method to design minimal phase digital filters with arbitrary amplitude characteristics. In: Corchado, E., Kurzyński, M., Woźniak, M. (eds.) HAIS 2011, Part I. LNCS, vol. 6678, pp. 67–74. Springer, Heidelberg (2011)
STMicroelectronics, AN2874 Applications note, February 2009
Tiwari, S., Koch, P., Fadel, G., Deb, K.: Amga: an archive-based micro genetic algorithm for multi-objective optimization. In: Proceedings of the 10th Annual Genetic and Evolutionary Computation Conference, Atlanta, USA 12–16 July, pp. 729–736 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Slowik, A. (2016). On Fast Randomly Generation of Population of Minimal Phase and Stable Biquad Sections for Evolutionary Digital Filters Design Methods. In: Nguyen, N.T., Trawiński, B., Fujita, H., Hong, TP. (eds) Intelligent Information and Database Systems. ACIIDS 2016. Lecture Notes in Computer Science(), vol 9621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49381-6_49
Download citation
DOI: https://doi.org/10.1007/978-3-662-49381-6_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-49380-9
Online ISBN: 978-3-662-49381-6
eBook Packages: Computer ScienceComputer Science (R0)