, Volume 8, Issue 3–4, pp 335–342 | Cite as

Polynomial Chebyshev approximation of a complex transfer function

  • C. Dierick
  • Y. Kamp


The characterization theorems ofRemez andVidensky for the polynomialChebyshev approximation of complex valued functions are reformulated for the particular case where the approximation is performed along the imaginary axis. When the characteristic set hasn+1 points (approximating polynomial of degreen−1) it is shown that the problem can be reduced to aChebyshev approximation and an interpolation of two real functions which are obtained by projection of the equations on a suitably rotated reference system. Based on these results, an algorithm is derived and then applied to numerical examples.


Transfer Function Computational Mathematic Reference System Real Function Degreen 
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Polynomiale Tschebyscheff Approximationen komplexer Funktionen


Der Charakterisierungssatz vonRemez undVidensky für polynomialeTschebyscheff-Approximationen komplexer Funktionen wird im Sonderfall einer Approximation auf der imaginären Achse formuliert. Wenn die Minimallösung (n+1) Extremalpunkte hat (Approximation mit Polynomenn-ten Grades), zeigt man, daß sich die Approximationsaufgabe auf eineTschebyscheff-Approximation und die Interpolation zweier reeller Funktionen reduzieren läßt, die durch Projektion auf entsprechend gedrehte Koordinatenachsen erhalten werden. Mit diesen Ergebnissen wird zunächst ein numerisches Verfahren konstruiert, das schließlich an Beispielen geprüft wird.


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Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • C. Dierick
    • 1
  • Y. Kamp
    • 1
  1. 1.M.B.L.E. Research LaboratoryBrussels 17Belgium

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