Design of 2-D IIR Filters Using Two Error Criteria with Genetic Algorithm

  • Felicja Wysocka-Schillak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4431)

Abstract

The paper presents a method for designing 2-D IIR filters with a quadrantally symmetric magnitude response. The method is based on two error criteria, i.e., equiripple error criterion in the passband and least-squared error criterion in the stopband. Two objective functions are introduced and the filter design problem is transformed into an equivalent bicriterion optimization problem. The stability of the filter is ensured by explicitly including stability constraints in the considered optimization problem. A two-step solution procedure of the considered problem is proposed. In the first step, a genetic algorithm is applied. The final point from the genetic algorithm is used as the starting point for a local optimization method. Two design examples are given to illustrate the proposed technique. A comparison with a 2-D IIR filter designed using LS approach is also presented.

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References

  1. 1.
    Adams, J.W., Sullivan, J.L.: Peak-Constrained Least-Squares Optimization. IEEE Trans. Signal Processing I 46, 306–320 (1998)CrossRefGoogle Scholar
  2. 2.
    Dumitrescu, B.: Optimization of Two-Dimensional IIR Filters with Nonseparable and Separable Denominator. IEEE Trans. on Signal Processing 53, 1768–1777 (2005)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison Wesley, New York (1989)MATHGoogle Scholar
  4. 4.
    Gorinevsky, D., Boyd, S.: Optimization-Based Design and Implementation of Multi-Dimensional Zero-Phase IIR filters. IEEE Trans. on Circuits and Syst. I 52, 1–12 (2005)Google Scholar
  5. 5.
    Gu, Q., Swamy, M.N.S.: On the Design of a Board Class of 2-D Recursive Digital Filters with Fan, Diamond and Elliptically Symmetric Responses. IEEE Trans. Circuits and Syst. II 41, 603–614 (1994)CrossRefGoogle Scholar
  6. 6.
    Karivaratharajan, P., Swamy, M.N.S.: Quadrantal Symmetry Associated with Two-Dimensional Transfer Functions. IEEE Trans. on Circuits and Syst. 25, 340–343 (1978)MATHCrossRefGoogle Scholar
  7. 7.
    Lim, J.S.: Two-Dimensional Signal and Image Processing. Prentice-Hall, Englewood Cliffs (1990)Google Scholar
  8. 8.
    Lu, W.-S., Hinamoto, T.: Optimal Design of IIR Digital Filters with Robust Stability Using Conic-Quadratic-Programming Updates. IEEE Trans. on Signal Processing 51, 1581–1592 (2003)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Lu, W.-S., Pei, S.-C., Tseng, C.-C.: A Weighted Least-Squares Method for the Design of Stable 1-D and 2-D IIR Digital Filters. IEEE Trans. on Signal Processing 46, 1–10 (1998)CrossRefGoogle Scholar
  10. 10.
    Lu, W.-S., Antoniou, A.: Minimax Design of 2-D IIR Digital Filters Using Sequential Semidefinite Programming. In: Proc. Int. Symp. Circuits Syst. III, pp. 353–356 (2002)Google Scholar
  11. 11.
    Lu, W.-S.: A Unified Approach for the Design of 2-D Digital Filters via Semidefinite Programming. IEEE Trans. on Circuits and Syst. I 45, 814–826 (2002)CrossRefGoogle Scholar
  12. 12.
    Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, Heidelberg (1999)MATHGoogle Scholar
  13. 13.
    Reddy, H.C., Khoo, I.-H., Rajan, P.K.: 2-D Symmetry: Theory and Filter Design Applications. IEEE Circuits and Syst. Mag. 3, 4–32 (2003)CrossRefGoogle Scholar
  14. 14.
    Shenoi, B.A., Misra, P.: Design of Two-Dimensional IIR Digital Filters with Linear Phase. IEEE Trans. Circuits and Syst. II 42, 124–129 (1995)CrossRefGoogle Scholar
  15. 15.
    Wysocka-Schillak, F.: Design of 2-D FIR Centro-Symmetric Filters With Equiripple Passband and Least-Squares Stopband. In: Proc. of the Europ. Conf. on Circuit Theory and Design, Cracow, Poland, vol. 3, pp. 113–116 (2003)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Felicja Wysocka-Schillak
    • 1
  1. 1.University of Technology and Life Sciences, Institute of Telecommunications, al. Prof. S. Kaliskiego 7, 85-796 BydgoszczPoland

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