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An approximation of Daubechies wavelet matrices by perfect reconstruction filter banks with rational coefficients

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Abstract

It is described how the coefficients of Daubechies wavelet matrices can be approximated by rational numbers in such a way that the perfect reconstruction property of the filter bank be preserved exactly.

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References

  1. Daubechies, I.: Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41, 909–996 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  2. Daubechies, I.: Ten Lectures on Wavelets. SIAM, Philadelhia, PA (1992)

    Book  MATH  Google Scholar 

  3. Delsarte, P., Gelin, Y., Kamp, Y.: A simple approach to spectral factorization. IEEE Trans. Circuits Syst. 25, 943–946 (1978)

    Article  MATH  Google Scholar 

  4. Ephremidze, L., Janashia, G., Lagvilava, E.: On the factorization of unitary matrix-functions. Proc. A. Razmadze Math. Inst. 116, 101–106 (1998)

    MathSciNet  MATH  Google Scholar 

  5. Ephremidze, L., Janashia, G., Lagvilava, E.: A simple proof of matrix-valued Fejér–Riesz theorem. J. Fourier Anal. Appl. 15, 124–127 (2009). doi:10.1007/s00041-008-9051-z

    Article  MathSciNet  MATH  Google Scholar 

  6. Ephremidze, L., Lagvilava, E.: On parameterization of compact wavelet matrices. Bull. Georgian Nat. Acad. Sci. 2(4), 23–27 (2008)

    MathSciNet  MATH  Google Scholar 

  7. Janashia, G., Lagvilava, E.: A method of approximate factorization of positive definite matrix functions. Stud. Math. 137(1), 93–100 (1999)

    MathSciNet  MATH  Google Scholar 

  8. Janashia, G., Lagvilava, E., Ephremidze, L.: A new method of matrix spectral factorization. IEEE Trans. Inf. Theory 57(4), 2318–2326 (2011). doi:10.1109/TIT.2011.2112233

    Article  MathSciNet  Google Scholar 

  9. Mallat, S.: A Wavelet Tour of Signal Processing. Academic, New York (1998)

    MATH  Google Scholar 

  10. Resnikoff, H.L., Wells, R.O.: Wavelet Analysis. Springer (1998)

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Authors and Affiliations

  1. A. Razmadze Mathematical Institute, University Street, Tbilisi, 0143, Georgia

    L. Ephremidze & E. Lagvilava

  2. I. Javakhishvili State University, University Street, Tbilisi, 0143, Georgia

    A. Gamkrelidze

Authors
  1. L. Ephremidze
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  2. A. Gamkrelidze
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  3. E. Lagvilava
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Corresponding author

Correspondence to A. Gamkrelidze.

Additional information

Communicated by Charles Micchelli.

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Ephremidze, L., Gamkrelidze, A. & Lagvilava, E. An approximation of Daubechies wavelet matrices by perfect reconstruction filter banks with rational coefficients. Adv Comput Math 38, 147–158 (2013). https://doi.org/10.1007/s10444-011-9232-1

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  • DOI: https://doi.org/10.1007/s10444-011-9232-1

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