Fourier Transformation

  • Philipp O. J. Scherer
Part of the Graduate Texts in Physics book series (GTP)


Fourier transformation is a very important tool for signal analysis but also helpful to simplify the solution of differential equations or the calculation of convolution integrals. An important numerical method is the discrete Fourier transformation which can be used for trigonometric interpolation and also as a numerical approximation to the continuous Fourier integral. It can be realized efficiently by Goertzel’s algorithm or the family of fast Fourier transformation methods. For real valued even functions the computationally simpler discrete cosine transformation can be applied. Several computer experiments demonstrate the principles of trigonometric interpolation and nonlinear filtering.


Discrete Cosine Transformation Discrete Fourier Transformation Trigonometric Function Fourier Component Transmission Function 
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  1. 2.
    N. Ahmed, T. Natarajan, K.R. Rao, IEEE Trans. Comput. 23, 90 (1974) MathSciNetzbMATHCrossRefGoogle Scholar
  2. 62.
    J.W. Cooley, J.W. Tukey, Math. Comput. 19, 297 (1965) MathSciNetzbMATHCrossRefGoogle Scholar
  3. 74.
    P. Duhamel, M. Vetterli, Signal Process. 19, 259 (1990) MathSciNetzbMATHCrossRefGoogle Scholar
  4. 103.
    G. Goertzel, Am. Math. Mon. 65, 34 (1958) MathSciNetzbMATHCrossRefGoogle Scholar
  5. 119.
    F.j. Harris, Proc. IEEE 66, 51 (1978) ADSCrossRefGoogle Scholar
  6. 144.
    E.I. Jury, Theory and Application of the Z-Transform Method (Krieger, Melbourne, 1973). ISBN 0-88275-122-0 Google Scholar
  7. 187.
    H.J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms (Springer, Berlin, 1990) Google Scholar
  8. 211.
    K.R. Rao, P. Yip, Discrete Cosine Transform: Algorithms, Advantages, Applications (Academic Press, Boston, 1990) zbMATHGoogle Scholar
  9. 268.
    Z. Wang, B.R. Hunt, Appl. Math. Comput. 16, 19 (1985) MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Philipp O. J. Scherer
    • 1
  1. 1.Physikdepartment T38Technische Universität MünchenGarchingGermany

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