Wavelets polynomials and associated zeros locations

Abstract

There are conditions imposed on the coefficients of filters and therefore on the roots of the binomial polynomials associated with the construction of Daubechies Wavelets. 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 along with some illustrations.