  We present a general setting where wavelet filters and multiresolution
decompositions can be defined, beyond the classical $\mathbf L^2(\mathbb R,dx)$
setting. This is done in a framework of {\em iterated function system} (IFS)
measures; these include all cases studied so far, and in particular the Julia
set/measure cases. Every IFS has a fixed order, say $N$, and we show that the
wavelet filters are indexed by the infinite dimensional group $G$ of functions
from $X$ into the unitary group $U_N$. We call $G$ the loop group because of
the special case of the unit circle.
