On the Distribution of Zeros for Daubechies Orthogonal Wavelets and Associated Polynomials

In the last decade, Daubechies orthogonal wavelets have been successfully used in many signal processing paradims. 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 it should exhibit. In this paper, a subclass of polynomials is derived from this construction process by considering the ratios of consecutive binomial polynomials’ coefficients. We show mathematically that the roots of this class of polynomials reside inside the unit circle and present an illustration for db6, a member of the Daubechies orthogonal wavelets family.