Recursive Filters

  • Robert King
  • Majid Ahmadi
  • Raouf Gorgui-Naguib
  • Alan Kwabwe
  • Mahmood Azimi-Sadjadi

Abstract

In this chapter we shall discuss techniques for designing recursive digital filters, with the restriction that the designed filter be realizable and stable. Part One of this chapter deals with different approaches for the design of one-dimensional (1-D) recursive filters.

Keywords

Butterworth Filter Magnitude Response Analogue Filter Prototype Filter Recursive Filter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    L. R. Rabiner, N. Y. Graham, and M. D. Helms, Linear programming design of IIR digital filters with arbitrary magnitude function, IEEE Trans. Acoust., Speech, Signal Process. ASSP-22, 117–123 (1974).CrossRefGoogle Scholar
  2. 2.
    L. R. Rabiner and B. Gold, Theory and Application of Digital Signal Processing, Prentice-Hall, Englewood Cliffs, NJ (1975).Google Scholar
  3. 3.
    A. Chottera and G. A. Jullien, Designing Near Linear Phase Recursive Filters Using Linear Programming, Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, 88-92 (May 1977).Google Scholar
  4. 4.
    E. I. Jury, Theory and Application of the z-Transform Method, John Wiley and Sons, New York (1964).Google Scholar
  5. 5.
    E. Robinson, Statistical Communication and Detection, Hafner, New York (1967).Google Scholar
  6. 6.
    F. H. Borphy and A. C. Salazar, Two design techniques for digital phase networks, Bell Syst. Tech. J. 54, 767–781 (1975).Google Scholar
  7. 7.
    V. Ramachandran and C. S. Gargour, Implementation of a stability test of 1-D discrete system based on Schussler’s theorem and some consequent coefficient conditions, J. Franklin Inst. 317, 341–358 (1984).MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    V. Ramachandran, C. S. Gargour, M. Ahmadi, and M. T. Boraie, Direct design of recursive digital filters based on a new stability test, J. Franklin Inst. 318, 407–413 (1984).MATHCrossRefGoogle Scholar
  9. 9.
    Lonnie C. Ludeman, Fundamentals of Digital Signal Processing, Harper and Row, New York (1986).Google Scholar
  10. 10.
    A. Antoniou, Digital Filters: Analysis and Design, McGraw-Hill, New York (1979).Google Scholar
  11. 11.
    A. Antoniou, M. Ahmadi, and C. Charalambous, Design of factorable lowpass 2-dimensional digital filters satisfying prescribed specifications, IEE Proc. 128, Part G, No. 2, 53–60 (1981).Google Scholar
  12. 12.
    C. Charalambous, Design of 2-dimensional circularly-symmetric digital filters, IEE Proc. 129, Part G, No. 2, 47–54 (1982).Google Scholar
  13. 13.
    K. Rajan and M. N. S. Swamy, Design of separable denominator 2-dimensional digital filters possessing real circularly symmetric frequency responses, IEE Proc. 129, Part G, No. 5, 235–240 (1982).Google Scholar
  14. 14.
    M. Ahmadi, M. T. Boraie, V. Ramachandran, and C. S. Gargour, Design of 2-D recursive digital filters with constant group delay characteristics using separable denominator transfer function and a new stability test, IEEE Trans. Acoust., Speech, Signal Process. ASSP-33, 1316–1318 (1985).MathSciNetCrossRefGoogle Scholar
  15. 15.
    T. S. Huang, J. W. Burnett, and A. G. Deczky, The importance of phase in image processing filters, IEEE Trans. Acoust, Speech, Signal Process. ASSP-23, 529–542 (1975).CrossRefGoogle Scholar
  16. 16.
    J. L. Shanks, S. Treitel, and J. M. Justice, Stability and synthesis of two-dimensional recursive filters, IEEE Trans. Audio Electroacoust. AU-20, 115–128 (1982).Google Scholar
  17. 17.
    J. M. Costa and A. N. Venetsanopoulos, Design of circularly symmetric two-dimensional recursive filters, IEEE Trans. Acoust, Speech, Signal Process. ASSP-22, 432–443 (1974).CrossRefGoogle Scholar
  18. 18.
    M. Ahmadi, A. G. Constantinides, and R. A. King, Design Technique for a Class of Stable 2-Dimensional Recursive Digital Filters, Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, Philadelphia, USA, 145-147 (April 1976).Google Scholar
  19. 19.
    R. A. King and A. H. Kayran, A New Transformation Technique for the Design of 2-Dimensional Stable Recursive Digital Filters, Proc. IEEE Int. Symp. on Circuits and Systems, Chicago, 196-199 (April 1981).Google Scholar
  20. 20.
    A. H. Kayran and R. A. King, Design of recursive and nonrecursive fan filters with complex transformations, IEEE Trans. Circuits Syst. CAS-30, 849–857 (1983).CrossRefGoogle Scholar
  21. 21.
    A. Chottera and G. A. Jullien, Design of 2-dimensional recursive digital filters using linear programming, IEEE Trans. Circuits Syst. CAS-29, 817–826 (1982).MathSciNetCrossRefGoogle Scholar
  22. 22.
    R. Fletcher and M. J. D. Powell, A Rapid descent method for minimization, Comput. J. 6, 163–168 (1963).MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    S. A. H. Aly and M. M. Fahmy, Design of two-dimensional recursive digital filters with specified magnitude and group delay characteristics, IEEE Trans. Circuits Syst. CAS-25, 908–916 (1978).CrossRefGoogle Scholar
  24. 24.
    P. A. Ramamoorthy and L. T. Bruton, Design of stable two-dimensional analogue and digital filters with applications in image processing, Int. J. Circuit Theory Appl. 7, 229–245 (1979).MATHCrossRefGoogle Scholar
  25. 25.
    S. Golikeri, M. Ahmadi, and V. Ramachandran, Design of 2-D recursive digital filters satisfying prescribed magnitude and constant group delay response, Electron. Lett. 19, 9–11 (1983).CrossRefGoogle Scholar
  26. 26.
    V. Ramachandran and M. Ahmadi, Design of 2-D stable analog and recursive digital filters using properties of the derivative of even or odd parts of Hurwitz polynomials, J. Franklin Inst. 315, 259–267 (1983).MathSciNetMATHCrossRefGoogle Scholar
  27. 27.
    M. Ahmadi and V. Ramachandran, New method for generating two-variable VSHPs and its application in the design of two-dimensional recursive digital filters with prescribed magnitude and constant group delay responses, IEE Proc. 131, Part G, No. 4, 151–155 (1984).CrossRefGoogle Scholar
  28. 28.
    M. Ahmadi, M. O. Ahmad, and V. Ramachandran, Transfer function realization of a class of doubly-terminated two-variable lossless networks and their application in linear phase 2-dimensional filter design, J. Franklin Inst. 321, 147–153 (1986).MATHCrossRefGoogle Scholar
  29. 29.
    G. W. Bordner, Time Domain Design of Stable Recursive Digital Filters, Ph.D. Dissertation, State University of New York at Buffalo (1974).Google Scholar

Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • Robert King
    • 1
  • Majid Ahmadi
    • 2
  • Raouf Gorgui-Naguib
    • 3
  • Alan Kwabwe
    • 4
  • Mahmood Azimi-Sadjadi
    • 5
  1. 1.Imperial CollegeLondonEngland
  2. 2.University of WindsorWindsorCanada
  3. 3.University of Newcastle upon TyneNewcastle upon TyneEngland
  4. 4.Imperial College and Bankers Trust CompanyLondonEngland
  5. 5.Colorado State UniversityFort CollinsUSA

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