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Refining Oscillatory Signals by Non—Stationary Subdivision Schemes

  • Nira Dyn
  • David LevinAriel Luzzatto
Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 145)

Abstract

The paper presents a method for refining real highly oscillatory signals. The method is based upon interpolation by a finite set of trigonometric basis functions. The set of trigonometric functions is chosen (identified) by minimizing a natural error norm in the Fourier domain. Both the identification and the refining processes are computed by linear operations. Unlike the Yule—Walker approach, and related algorithms, the identification of the approximating trigonometric space is not repeated for every new input signal. It is rather computed off—line for a family of signals with the same support of their Fourier transform, while the refinement calculations are done in real—time. Statistical estimates of the point—wise errors are derived, and numerical examples are presented.

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References

  1. 1.
    K. Clarke, D. Hess: Communication Circuits, Analysis and Design, Addison Wesley, 1978.Google Scholar
  2. 2.
    N. Dyn, D. Levin: Subdivision schemes in geometric modeling, Acta Numerica (2002), 73–144.Google Scholar
  3. 3.
    N. Dyn, D. Levin, A. Luzzatto: Non-stationary interpolatory subdivision schemes reproducing spaces of exponential polynomials, To appear.Google Scholar
  4. 4.
    A. Luzzatto: Multi-Scale Signal Processing based on Non-Stationary Subdivision, PhD Thesis, Tel-Aviv University, 2000.Google Scholar
  5. 5.
    M. Schwartz: Information, Transmission, Modulation and Noise, McGraw-Hill, 1990.Google Scholar

Copyright information

© Springer Basel AG 2003

Authors and Affiliations

  • Nira Dyn
    • 1
  • David LevinAriel Luzzatto
    • 1
    • 2
  1. 1.Tel-Aviv University School of Mathematical SciencesTel-AvivIsrael
  2. 2.Motorola Communications Israel 3 Kremenetzky stTel-AvivIsrael

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