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J. Karam, “Connecting Daubechies Wavelets with the Kakeya-Enestrom Theorem,” International Journal of Applied Mathematics, Vol. 14, No. 2, 2003, pp. 109-124.

has been cited by the following article:

• TITLE: On the Zeros of Daubechies Orthogonal and Biorthogonal Wavelets

  AUTHORS: Jalal Karam

  KEYWORDS: Orthogonal; Biorthogonal Wavelets; Binomial Polynomials

  JOURNAL NAME: Applied Mathematics, Vol.3 No.7, June 19, 2012

  ABSTRACT: In the last decade, Daubechies’ wavelets have been successfully used in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. In this paper, orthogonal and Biorthogonal Daubechies families of wavelets are considered and their filters are derived. In particular, the Biorthogonal wavelets Bior3.5, Bior3.9 and Bior6.8 are examined and the zeros distribution of their polynomials associated filters are located. We also examine the locations of these zeros of the filters associated with the two orthogonal wavelets db6 and db8.