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Degree of rational approximation in digital filter realization

  • Charles K. Chui
  • Xie-Chang Shen
Circuit Theory
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)

Abstract

In recursive digital filter design, the amplitude characteristic of an ideal filter has to be translated into a rational function that is pole-free on the closed unit disk and preferably has real coefficients. This is possible through a causal transformation utilizing the tolerance allowance. In this paper we study the degree of uniform approximation by rational functions that fulfill the filter criteria and can be computed by interpolation or the method of least-squares inverses.

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References

  1. 1.
    Chui, C. K. and Chan, A. K., Application of approximation theory methods to recursive digital filter design, IEEE Trans. on ASSP, 30 (1982), 18–24.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Robinson, E. A, Statistical Communication and Detection, Hafner, New York, 1967.Google Scholar
  3. 3.
    Rusak, V. N., Direct methods in rational approximation with free poles, Dokl. Akad. Nauk BSSR, 22 (1978), 18–20.MathSciNetzbMATHGoogle Scholar
  4. 4.
    Rusak, V. N., Rational Functions as Approximation Apparatus, Beloruss. Gos. Univ., Minsk, 1979.Google Scholar
  5. 5.
    Suetin, P. K., Fundamental properties of polynomials orthogonal on a contour, Russian Math. Surveys, 21 (1966), 35–84.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Szabados, J., Rational approximation in complex domain, Studia Sci. Math. Hungarian, 4 (1969), 335–340.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Szabados, J., Rational approximation to analytic functions on an inner part of the domain of analyticity, in Approximation Theory, ed. by A. Talbot, Academic Press, New York, 1970, pp. 165–177.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Charles K. Chui
    • 1
  • Xie-Chang Shen
    • 2
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA
  2. 2.Department of MathematicsPeking UniversityBeijingChina

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