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Magnitude and Delay Approximation of 2-D IIR Filters

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Magnitude and Delay Approximation of 1-D and 2-D Digital Filters

Part of the book series: Digital Signal Processing ((DIGSIGNAL))

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Abstract

In this chapter, we will discuss a few methods that are available for the design of two-dimensional (2-D) IIR filters which approximate not only a specified magnitude response but also a constant group delay. The first three methods assume a certain structure for the desired transfer function that allows the computer-aided optimization procedure to assure stability of the 2-D filter. Optimization of a suitably defined performance index (objective function) is carried out such that the magnitude and group delay are approximated in either maximally flat, or equiripple sense but more often in the least squares sense. Depending on the performance index chosen and the optimization criteria, the complexity of computation can be very high; but irrespective of such choices, there is always the problem of choosing an optimal order for the desired filter. If only the magnitude is to be approximated and the specified response is piece-wise constant over finite regions like circular, or elliptic regions in the ω1 — ω2 plane, then these approximation techniques have to try different order for the filter and choose the ‘best’ design that meets the magnitude specifications. These three methods can be applied to the design of 1-D IIR filters as a special case of the 2-D IIR filter approximation problem. In turn, these methods can be viewed as extensions of the methods used for approximating the magnitude and group delay response of the 1-D IIR filters.

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Bibliography

  1. S.A.H. Aly and M.M. Fahmy, “Design of two-dimensional recursive digital filters with specified magnitude and group delay characteristics,” IEEE Trans. on Circuits and Systems, CAS-25, pp. 908–915, November 1978.

    Article  Google Scholar 

  2. J.A. Cadzow, “Recursive digital filter synthesis via gradient based algorithms,” IEEE Trans. on Acoustics, Speech and Signal Processing, ASSP24, pp. 349–355, October 1976.

    Article  Google Scholar 

  3. S. Chakrabarti and S.K. Mitra, “Design of two-dimensional digital filters via spectral transformations,” Proc. IEEE, vol. 65, no. 6, pp. 905–914, June 1977.

    Article  Google Scholar 

  4. H. Chang and J.K. Aggarwal, “ Design of 2-dimensional recursive filters by interpolation,” Proc. IEEE Int’l Symposium on Circuits and Systems, pp. 369–372, April 1976.

    Google Scholar 

  5. A.T. Chottera and G.A. Jullien, “Design of two-dimensional recursive digital filters using Linear Programming,” IEEE Trans. on Circuits and Systems CAS-29, pp. 817–826, December 1982.

    Article  MathSciNet  Google Scholar 

  6. A.T. Chottera and G.A. Jullien, “A Linear Programming approach to recursive digital filter design with linear phase,” IEEE Trans. on Circuits and Systems, CAS-29, pp. 139–149, December 1982.

    Article  MathSciNet  Google Scholar 

  7. A.G. Constantinides, “Spectral transformations for digital filters,” Proc. IEE, vol. 117, pp. 1585–1590, 1970.

    Google Scholar 

  8. J.M. Costa and A.N. Venetsanopolous, “Design of circularly symmetric two-dimensional recursive filters,” IEEE Trans. on Acoustics, Speech and Signal Processing, ASSP-22, pp. 432–443, December 1974.

    Article  Google Scholar 

  9. R. Fletcher, Practical Methods of Optimization, (2nd edition) Chichester, John Wiley, 1987

    Google Scholar 

  10. R. Fletcher and M.J.D. Powell, “A rapidly convergent descent method for minimization,” Comput. Journal, vol. 6, no. 2, pp. 163–168, 1963.

    Article  MathSciNet  MATH  Google Scholar 

  11. D.M. Goodman, “A design technique for circularly symmetric lowpass filters,” IEEE Trans. on Acoustics, Speech and Signal Processing, ASSP-26, pp. 290–303, August 1978.

    Article  Google Scholar 

  12. G. Gu and B.A. Shenoi, “A novel approach to the synthesis of recursive digital filters with linear phase,” IEEE Trans. on Circuits and Systems, vol. 38, pp. 602–612, June 1991.

    Article  Google Scholar 

  13. G. Gu, B.A. Shenoi and C. Zhang, “Synthesis of 2-D linear phase digital filters,” IEEE Trans. on Circuits and Systems, vol. 37, pp. 1499–1508, December 1990.

    Article  MATH  Google Scholar 

  14. L. Ham and B.A. Shenoi, “Design of stable two-dimensional IIR filters using digital spectral transformations,” IEEE Trans. on Circuits and Systems, CAS-33, pp. 483–490, May 1986.

    Google Scholar 

  15. Rajamohana Hegde and B.A. Shenoi, “Design of 2-D IIR filters using a new digital spectral transformation,” Proc. IEEE Int’l Symposium on Circuits and Systems, vol II, pp. 344–347, May 1995.

    Google Scholar 

  16. -ibid-, “A unified approach to the design of 2-D IIR digital filters with flat passband magnitude and delay characteristics,” Proc. IEEE Int’l Sympo. on Circuits and Systems, vol. I, pp. 765–768, 1997.

    Google Scholar 

  17. Rajamohana Hegde and B.A. Shenoi, “Magnitude approximation of IIR digital filters with constant group delay response,” Proc. IEEE Int’l Sympo. on Circuits and Systems, vol. IV, pp. 2200–2203, 1997.

    Google Scholar 

  18. Rajamohana Hegde and B.A. Shenoi, “Magnitude approximation of digital filters with specified degrees of flatness and constant group delay characteristics,” IEEE Trans. on Circuits and Systems: Part II. (To be published)

    Google Scholar 

  19. T. Hinamoto and S. Maekawa, “Design of two-dimensional recursive digital filters using mirror image polynomials,” IEEE Trans. on Circuits and Systems, CAS-33, pp. 750–758, August 1986.

    Article  Google Scholar 

  20. T.S. Huang, J.W. Burnett, and A.G. Deczky, “The importance of phase in image processing filters,” IEEE Trans. on Acoustics, Speech and Signal Processing, ASSP-23, pp. 529–542, December 1975.

    Article  Google Scholar 

  21. H.K. Kwan and C.L. Chan, “Multidimensional spherically symmetric recursive digital filter design satisfying prescribed magnitude and constant group delay response,” Proc.IEE, Pt.G: Electronic Circuits and Systems, pp. 187–193, August 1987.

    Google Scholar 

  22. H.K. Kwan and C.L. Chan, “Design of two-dimensional circularly symmetric IIR digital low-pass filters by spectral transformation,” Proc.IEEE Asian Electronics Conference, Hong Kong, pp. 29–33, 1987.

    Google Scholar 

  23. H.K. Kwan and C.L. Chan, “Design of linear phase circularly symmetric two-dimensional recursive digital filters,” IEEE Trans. on Circuits and Systems, CAS-36;, pp. 1023–1029, July 1989.

    Article  Google Scholar 

  24. J.S. Lim, Two-Dimensional Signal and Image Processing, Prentice- Hall, 1990.

    Google Scholar 

  25. G.V. Mendonca, A. Antoniou and A.N. Venetsanoplous, “Design of two-dimensional pseudorotated digital filters satisfying prescribed specifications,” IEEE Trans. on Circuits and Systems, CAS-34, pp. 1–10, January 1987.

    Article  Google Scholar 

  26. K. Nishikawa and R.M. Mersereau, “Design of circularly symmetric two-dimensional IIR lowpass digital filters with constant group delay using McClellan Transformation,” Trans. IEICE, vol. E75-A, pp. 830–836, July 1992.

    Google Scholar 

  27. T.Q. Nguyen, T.I. Laakso and R.D. Koilpillai, “Eigenfilter approach for the design of allpass filters approximating a given phase response,” IEEE Trans. on Signal Processing, vol. 42, pp. 2257–2263, September 1994.

    Article  Google Scholar 

  28. N.A. Pendergrass, S.K. Mitra and E.I. Jury, “Spectral transformations for two-dimensional digital filters,” IEEE Trans. on Circuits and Systems, vol. CAS-23, pp. 26–35, January 1976.

    Article  MathSciNet  Google Scholar 

  29. P.K. Rajan and M.N.S. Swamy, “Quadrantal symmetry associated with two-dimensional digital transfer functions,” IEEE Trans. on Circuits and Systems, CAS-25, pp. 340–343, June 1978.

    Google Scholar 

  30. P.A. Ramamoorthy and L.T. Bruton, “Frequency domain approximation of stable multi-dimensional discrete recursive filters,” Proc.of Int’l Symp. on Circuits and Systems, pp. 654–657, April 1977.

    Google Scholar 

  31. P.A. Ramamoorthy and L.T. Bruton, Chapter 3: Design of Two-Dimensional Recursive Filters, Digital Signal Processing.(T.S.Huang, Editor) Springer-Verlag, 1981

    Google Scholar 

  32. B.A. Shenoi and P. Mitra, “Design of two-dimensional IIR digital filters with linear phase,” IEEE Trans. on Circuits and Systems-II, vol. 42, pp. 124–129, February 1995.

    Article  Google Scholar 

  33. J.P. Thiran, “Recursive digital filters with maximally flat group delay,” IEEE Trans. on Circuit Theory, vol. CT-18, pp. 659–663, November 1971.

    Article  MathSciNet  Google Scholar 

  34. A.N. Venetsanopolous, Chapter 12: Computer-Aided Design of Two-Dimensional Digital Filters, Multidimensional Systems-Techniques and Applications(S.G.Tzafestas, Editor ), Marcel Dekker Inc, 1986.

    Google Scholar 

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Authors and Affiliations

  1. Electrical Engineering Department, Wright State University, 3640 Colonel Glenn Highway, Dayton, Ohio, 45435-0001, USA

    Professor Dr. Belle A. Shenoi

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  1. Professor Dr. Belle A. Shenoi
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© 1999 Springer-Verlag Berlin Heidelberg

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Shenoi, B.A. (1999). Magnitude and Delay Approximation of 2-D IIR Filters. In: Magnitude and Delay Approximation of 1-D and 2-D Digital Filters. Digital Signal Processing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58573-9_4

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  • DOI: https://doi.org/10.1007/978-3-642-58573-9_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63652-3

  • Online ISBN: 978-3-642-58573-9

  • eBook Packages: Springer Book Archive

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