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Expansions of Functions Based on Rational Orthogonal Basis with Nonnegative Instantaneous Frequencies

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  • Xiaona Cui
  • Suxia Yao

Abstract

We consider in this paper expansions of functions based on the rational orthogonal basis for the space of square integrable functions. The basis functions have nonnegative instantaneous frequencies so that the expansions make physical sense. We discuss the almost everywhere convergence of the expansions and develop a fast algorithm for computing the coefficients arising in the expansions by combining the characterization of the coefficients with the fast Fourier transform.

Suggested Citation

  • Xiaona Cui & Suxia Yao, 2014. "Expansions of Functions Based on Rational Orthogonal Basis with Nonnegative Instantaneous Frequencies," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-6, August.
    • Handle: RePEc:hin:jnljam:526940
    DOI: 10.1155/2014/526940
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