Fast communication: Pascal's triangle: An origin of Daubechies polynomials and an analytic expression for associated filter coefficients

  • Authors:

  • Angel Scipioni;Pascal Rischette;Jean-Philippe Préaux

  • Affiliations:

  • Laboratoire d'Instrumentation Electronique de Nancy, Nancy Université, BP 239, F-54506 Vanduvre-lès-Nancy cedex, France;Laboratoire d'Instrumentation Electronique de Nancy, Nancy Université, BP 239, F-54506 Vanduvre-lès-Nancy cedex, France and Centre de recherche de l'Armée de l'air, BA701, F-13661 S ...;Centre de recherche de l'Armée de l'air, BA701, F-13661 Salon air, France and Laboratoire d'Analyse, Topologie, Probabilités - UMR CNRS 6632, 39 rue F. Joliot-Curie, F-13453 Marseille ce ...

  • Venue:
  • Signal Processing
  • Year:
  • 2012

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Abstract

After showing that Daubechies polynomial coefficients can be simply obtained from Pascal's triangle by some elementary additions, we propose a derivation of the spectral factorization by using the elementary symmetric functions. This derivation leads us to present an analytic expression, able to compute Daubechies wavelet filter coefficients from the roots of the associated Daubechies polynomial. Thus, these coefficients are directly obtained and without recurrence. At last, we measure the quality of the coefficient sets generated by this expression and we compare it with two well-known methods.