  In this paper we outline several points of view on the interplay between
discrete and continuous wavelet transforms; stressing both pure and applied
aspects of both. We outline some new links between the two transform
technologies based on the theory of representations of generators and
relations. By this we mean a finite system of generators which are represented
by operators in Hilbert space. We further outline how these representations
yield sub-band filter banks for signal and image processing algorithms.
