  In this paper, we study wavelet filters and their dependence on two numbers,
the scale N and the genus g. We show that the wavelet filters, in the
quadrature mirror case, have a harmonic analysis which is based on
representations of the C^*-algebra O_N. A main tool in our analysis is the
infinite-dimensional group of all maps T -> U(N) (where U(N) is the group of
all unitary N-by-N matrices), and we study the extension problem from low-pass
filter to multiresolution filter using this group.
