Rational filter wavelets

In this paper, we introduce two types of rational filters for the construct ion of wavelets. The rational filters are a natural development of the poly nomial filters. We use rational filters to derive a large family of the wav elets which can include Daubechies wavelets and Battle-Lemarie wavelets. Es pecially the II-type rational filter wavelets among the family have linear phases. Furthermore, we analyze the regularity of the rational filter wavel ets and estimate their regularity indices. Some examples are also given. (C ) 1999 Academic Press.