Genetic Algorithm for the Design of Optimal IIR Digital Filters
- 1 Department of Electronics and Communication Engineering, JMIT Radaur
- 2 Department of Electronics and Communication Engineering, GJUS&T
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.
- V. K. Ingle and J. G. Proakis, “Digital Signal Processing Using MATLAB,” Thomson Books, New Delhi, 2004.
- J. G. Proakis and D. G. Manolakis, “Digital Signal Processing: Principles, Algorithms, and Applications,” 4th Edition, Pearson Education, Inc., New Delhi, 2007.
- P. Tarasewich and P. R. McMullen, “Swarm Intelli- gence,” Communication of the ACM, Vol. 45, No. 8, 2002, pp. 62-67.
- L. Y. Cao, “Practical Issues in Implementing a Single- Pole Low-Pass IIR Filter,” IEEE Signal Processing Ma- gazine, November 2010, pp. 114-117.
- 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
- 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
- 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
- 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
- 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.
- 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
- 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
- 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
- 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
- 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.