Rational Filter Wavelets*

In this paper, we introduce two types of rational filters for the construction of wavelets. The rational filters are a natural development of the polynomial filters. We use rational filters to derive a large family of the wavelets which can include Daubechies wavelets and Battle]Lemari´e wavelets. Especially the II-type rational filter wavelets among the family have linear phases. Furthermore, we analyze the regularity of the rational filter wavelets and estimate their regularity indices. Some examples are also given.