**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30579

##### FIR Filter Design via Linear Complementarity Problem, Messy Genetic Algorithm, and Ising Messy Genetic Algorithm

**Authors:**
A.M. Al-Fahed Nuseirat,
R. Abu-Zitar

**Abstract:**

**Keywords:**
Filter Design,
Ising model,
FIR digital filters,
LCP,
MGA,
Ising MGA

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1058435

**References:**

[1] L. R. Rabiner, "The Design of Finite Impulse Response Digital Filters using Linear Programming Techniques", Bell Syst. Tech. J., 51, 1117-1198, 1972.

[2] P. P. Vaidyanathan and T. Q. Nguyen, "Eigenfilters: A New Approach to Least-Square FIR Filter Design and Applications Including Nyquist Filters", IEEE Trans. Circuits Syst., CAS-34 (1), 11 - 23, 1987.

[3] G. W. Medlin, J. W. Adams, and C. T. Leondes, "Lagrange Multiplier Approach to the Design of FIR Filters for Multirate Applications", IEEE Trans. Circuits Syst., 35, 1210 - 1219, 1988.

[4] M. H. Er and C. K. Siew, "Design of FIR Filters Using Quadratic Programming Approach", IEEE Trans. Circuits Syst. II, 42 (3), 217 - 220, 1995.

[5] E. Gislason, M. Johansen, K. Conradsen, B. K. Erboll, and S. K. Jacobsen, "Three Different Criteria for the Design of 2-D Zero-Phase FIR Digital Filters", IEEE Trans. Signal Processing, 41, 3070 -3074,1993.

[6] Y. C. Lim, J. H. Lee, C. K. Chen, and R. H. Yang, "A Weighted Least Square Algorithm for Quasi-Equiripple FIR and IIR Digital Filter Design", IEEE Trans. Signal Processing, 40, 551 -558, 1992.

[7] C. -H. Hseih, C. -M. Kuo, Y. -D Jou, and Y. L. Han, "`Design of Two- Dimensional FIR Digital Filters by Two-Dimensional WLS Technique",, IEEE Trans. Circuits Syst. II, 44, 348 - 358, 1997.

[8] V. R. Algazi, M. Suk, and C. -S. Rim, "Design of Almost Minimax FIR Filters in One and Two Dimensions by WLS Technique", IEEE Trans. Circuits Syst., CAS-33, 590 - 596, 1986.

[9] M. Lang, I. W. Selesnick, and C. S. Burrus, "Constrained Least Squares Design of 2-D FIR Filters", IEEE Trans. Signal Processing, 44, 1234 - 1241, 1996.

[10] W. P. Zhu, M. O. Ahmad, and M. N. S. Swamy, "A Closed-Form Solution to the Least-Square Design Problem of 2-D Linear-Phase FIR Filters", IEEE Trans. Circuits Syst. II, 44, 1032 - 1039, 1997.

[11] K. C. Haddad, H. Stark, and Nickolas P. Galatsanos, "Constrained FIR Filter Design by the Method of Vector Space Projection", IEEE Trans. Circuits Syst. II, 47, 714 - 725, 2000.

[12] W. P. Zhu, "Weighted Least-Square Design of FIR Filters Using a Fast Iterative Matrix Inversion Algorithm", IEEE Trans. Circuits Syst. I, 41 (11), 1620 - 1628, 2002.

[13] Magdy T. Hanna, "Design of Linear Phase FIR Filters with a Maximally Flat Passband", IEEE Trans. Circuits Syst. II, 43 (2), 142 - 147, 1996.

[14] J. Besag, "Spatial interaction and the statistical analysis of lattice systems (with discussions)", J. of the Royal Statistical Society, 36, 192 - 236, 1974.

[15] D. F. Brown, A. B. Garmendia-Doval, and J. A. W. McCall, "A genetic algorithm framework using Haskell", Proc. of the 2nd Asia-Pacific Conference on Genetic Algorithms, Global Link Publishing, May 2000.

[16] D. F. Brown, A. B. Garmendia-Doval, and J. A. W. McCall, "A functional frame-work for the implementation of genetic algorithms: comparing Haskell and Stan-dard ML.", In S. Gilmore, editor, Trends in Functional Programming, volume 2, pp., 27 - 37, Portland, Oregon. Intellect Books, 1999.

[17] H. Derin, and P. A. Kelly, "Discrete-index Markov-type random fields", Proc. of the IEEE, 77, 1485 - 1510, 1989.

[18] S. Z. Li, Markov Random Field Modelling in Computer Vision, Springer, 1995.

[19] N. Metropolis, "Equations of state calculations by fast computational machine", J. of Chemical Physics, 21, 1087 - 1091, 1953.

[20] M. Mitchell, J. H. Holland, and S. Forrest, "When will a genetic algorithm outper-form hillclimbing?", In J. D. Cowan, G. Tesauro, and J. Alspector, editors, Advances in Neural Information Processing Systems 6. Morgan Kaufmann, 1994.

[21] M. Pelikan, and D. E. Goldberg, "Research on theBayesian Optimization Algorithm", Technical Report 2000010, Illinois Genetic Algorithms Lab, UIUC, Urbana, IL, 2000.

[22] M. Pelikan, D. E. Goldberg, and E. Cant'u-Paz, "BOA: The Bayesian Optimization Algorithm", In W. Banzhaf et al., editor, Proc. of the Genetic and Evolution-ary Computation Conference (GECCO99), volume I, pp., 525 - 532, San Fransisco, CA. Morgan Kaufmann Publishers, 1999.

[23] M. Pelikan, D. E. Goldberg and F. Lobo, "A survey of optimization by building and using probabilistic models", Technical Report 99018, Illinois Genetic Algorithms Lab, UIUC, Urbana, IL, 1999.

[24] C.-T. Chen, Digital Signal Processing: Spectral Compuattion and Filter Design, Oxford Univ. Press, New York, 2001.

[25] E. C. Ifeachor and B. W. Jervis , Digital Signal Processing: A Practical Approach, Addison - Wesley, 1993.

[26] K. G. Murty, Linear Complementarity: Linear and Nonlinear Programming, Berlin: Heldermann Verlag, 1988.

[27] B. H. Ahn, "Solution of Nonsymmetric Linear Complementarity Problems by Iterative Methods", J. of Optimization Theory and Applications, 33(2), 175 - 185, 1981.