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Improving convergence for the approximation of non-periodic functions by Fourier series

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Abstract

Approximation of functions by Fourier series plays an important role in many applied problems of digital signal processing. An effective method is presented for the construction of highly accurate mean-square approximations by Fourier series for nonperiodic functions. This technique employs the subtraction of specially selected functions that enhance the smoothness of the periodic extension of the approximated function. The main advantage of the method is that the function-setting interval is taken as a half-period rather than a whole period. This doubles the smoothness of the periodic extension. The efficiency of the method is illustrated by test functions of one and two variables.

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References

  1. A. N. Krylov, On Approximate Calculations, 6th ed. (Gos. Izd. Tekh. Teor. Lit., Moscow, 1954).

    Google Scholar 

  2. B. Adcock, Modified Fourier Expansions: Theory, Construction and Application (Trinity Hall, Cambridge Univ. Press, Cambridge, 2010).

    Google Scholar 

  3. N. Ahmed and K. Rao, Orthogonal Transforms for Digital Signal Processing (Springer, Heidelberg, 1975).

    Book  MATH  Google Scholar 

  4. C. Lanczos, The Practical Methods of Applied Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1956).

    Google Scholar 

  5. N. N. Kalitkin and K. I. Lutskii, “The method of odd continuation for Fourier approximations of nonperiodic function,” Dokl. Math. 84(3), 866–871 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  6. R. V. Golovanov, N. N. Kalitkin, and K. I. Lutskii, “Odd extension for Fourier approximation of non-periodic functions,” Math. Models Comput. Simul. 5(6), 595–606 (2013).

    Article  MathSciNet  Google Scholar 

  7. N. N. Kalitkin and R. V. Golovanov, “Smoothed gradients criterion for image quality assessment,” Dokl. Math. 88(1), 495–498 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  8. N. N. Kalitkin, K. I. Lutskii, “Approximation of smooth surfaces with the double period method,” Math. Models Comput. Simul. 2(5), 593–596 (2010).

    Article  Google Scholar 

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Authors and Affiliations

  1. National Research University of Electronic Technology, Proezd 4806 5, Zelenograd, 124498, Russia

    R. V. Golovanov

  2. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, pl. Miusskaya 4, Moscow, 125047, Russia

    N. N. Kalitkin

Authors
  1. R. V. Golovanov
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  2. N. N. Kalitkin
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Correspondence to R. V. Golovanov.

Additional information

Original Russian Text © R.V. Golovanov, N.N. Kalitkin, 2014, published in Matematicheskoe Modelirovanie, 2014, Vol. 26, No. 2, pp. 108–118.

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Golovanov, R.V., Kalitkin, N.N. Improving convergence for the approximation of non-periodic functions by Fourier series. Math Models Comput Simul 6, 456–464 (2014). https://doi.org/10.1134/S2070048214050032

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  • DOI: https://doi.org/10.1134/S2070048214050032

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