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.
J. Karam, “Radial Basis Functions With Wavelet Packets For Recognizing Arabic Speech,” The 9th WSEAS International Conference on Circuits, Systems, Electronics, Control and Signal Processing, Athens, December 2010, pp. 34-39.
J. Karam, “On the Distribution of Zeros for Daubechies Orthogonal Wavelets and Associated Polynomials,” 15th WSEAS International Conference on Applied Mathematics, Athens, 29-31 December 2010, pp. 101-105.