Sharpening the limits of the zeros of Daubechies wavelets related polynomials

Abstract

The construction of Daubechies orthogonal mother wavelet 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 it should exhibit. In this paper, a particular class of polynomials is derived from such construction. It bears as coefficients the ratios of those of the binomial polynomials. Limits for the roots of this family of polynomials are derived and the conditions for obtaining optimum radius are identified.