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A new series representation derived for periodic functions that can be represented by the Fourier series

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Abstract

The Fourier series are, as we know, widely used in a number of mathematical problems arising in various topics of Communication systems, Signal Processing, Image processing and many more. The main contribution through these series is to analyze and build periodic functions in the form of infinite or finite sums of sines and cosines. In this paper, a new series representation like the Fourier series has been derived for every periodic function which can be represented by the Fourier series, thereby increasing the extent of applications of Fourier analysis in the related fields.

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References

  1. Li, W.L., Daniels, M.: A Fourier series method for the vibrations of elastically restrained plates arbitrarily loaded with springs and masses. J. Sound Vib. 252(4), 768–781 (2002)

    Article  Google Scholar 

  2. Layton, A.T., Spotz, W.F.: A semi-Lagrangian double Fourier method for the shallow water equations on the sphere. J. Comput. Phys. 189, 180–196 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  3. Li, W.L.: Comparison of Fourier sine and cosine series expansions for beams with arbitrary boundary conditions. J. Sound Vib. 255(1), 185–194 (2002)

    Article  Google Scholar 

  4. Cheong, H.B.: Double Fourier series on a sphere: applications to elliptic and vorticity equations. J. Comput. Phys. 157, 327–349 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gottlieb, D., Shu, C.W.: On the Gibbs phenomenon and its resolution. SIAM Rev 39(4), 644–668 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chung, M.K., Dalton, K.M., Shen, L., Evans, A.C., Davidson, R.J.: Weighted Fourier series representation and its application to quantifying the amount of gray matter. IEEE Trans. Med. Imaging 26(4), 566–581 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. Quarter No. A17/4, Goa University Quarters, Taleigao Plateau, Panaji, Goa, India

    Prateek Kulkarni

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  1. Prateek Kulkarni
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Correspondence to Prateek Kulkarni.

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Kulkarni, P. A new series representation derived for periodic functions that can be represented by the Fourier series. SeMA 68, 1–15 (2015). https://doi.org/10.1007/s40324-014-0028-3

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  • DOI: https://doi.org/10.1007/s40324-014-0028-3

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