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Fourier Transformation

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Book cover Computational Physics

Part of the book series: Graduate Texts in Physics ((GTP))

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Abstract

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.

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Notes

  1. 1.

    This could also be the periodic continuation of a function which is only defined for 0<t<T.

  2. 2.

    There exist several Fast Fourier Transformation algorithms [74, 187]. We consider only the simplest one here [62].

References

  1. N. Ahmed, T. Natarajan, K.R. Rao, IEEE Trans. Comput. 23, 90 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  2. J.W. Cooley, J.W. Tukey, Math. Comput. 19, 297 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  3. P. Duhamel, M. Vetterli, Signal Process. 19, 259 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Goertzel, Am. Math. Mon. 65, 34 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  5. F.j. Harris, Proc. IEEE 66, 51 (1978)

    Article  ADS  Google Scholar 

  6. E.I. Jury, Theory and Application of the Z-Transform Method (Krieger, Melbourne, 1973). ISBN 0-88275-122-0

    Google Scholar 

  7. H.J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms (Springer, Berlin, 1990)

    Google Scholar 

  8. K.R. Rao, P. Yip, Discrete Cosine Transform: Algorithms, Advantages, Applications (Academic Press, Boston, 1990)

    MATH  Google Scholar 

  9. Z. Wang, B.R. Hunt, Appl. Math. Comput. 16, 19 (1985)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Physikdepartment T38, Technische Universität München, Garching, Germany

    Philipp O. J. Scherer

Authors
  1. Philipp O. J. Scherer
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© 2013 Springer International Publishing Switzerland

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Scherer, P.O.J. (2013). Fourier Transformation. In: Computational Physics. Graduate Texts in Physics. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00401-3_7

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