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Periodic Splines and Fourier Analysis

  • Günter Meinardus
Chapter
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 49)

Abstract

The so-called discrete Fourier transform is introduced. Then the connection with Fourier coefficients of 2π-periodic functions is described. A theorem for some linear mapping leads to the theory of attenuation factors due to L. Collatz and W. Quade. Finally a new version of the Fast Fourier transform is presented.

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References

  1. [1]
    Collatz, L., Quade, W.: Zur Interpolationstheorie der reellen periodischen Funktionen. Sitzungsber. Preuss. Akad. Wiss. 30,383–429(1938),Google Scholar
  2. [2]
    Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19, 297–301 (1965).CrossRefzbMATHMathSciNetGoogle Scholar
  3. [3]
    Ehlich, H.: Untersuchungen zur numerischen Fourieranalyse. Math. Z. 91, 380 – 420 (1966).CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    Gautschi, W. Attenuation Factors in Practical Fourier Analysis. Numer. Math. 18, 373–400(1972).zbMATHMathSciNetGoogle Scholar
  5. [5]
    Meinardus, G.: Schnelle Fourier-Transformation. In: Numerische Methoden der Approximationstheorie Bd. 4. ISNM 42, edited by L. Collatz, G. Meinardus, H. Werner. Birkhäuser-Verlag Basel (1978).Google Scholar
  6. [6]
    Schüssler, H.W.: Digitale Systeme zur Signalverarbeitung. Springer-Verlag Berlin (1973).CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1979

Authors and Affiliations

  • Günter Meinardus
    • 1
  1. 1.University of SiegenWest Germany

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