  In this paper we want to show, that the finite impulse response quadratic
mirror filters (QMF) associated to a tower of grids $\Gamma\subset H=\bf Z^n$
can be identified with a right coset of the subgroup
Fix$(T_{\Gamma^{\perp}}$,Map$ ({\bf T}^n\to U(N)$: poly) of the group of
polynomial loops Map$({\bf T}^n\to U(N)$: poly) with $N=|H/\Gamma|$. The QMF
with some vanishing moments can be identified with cosets of subgroups. The
problem to parameterize all finite impulse response QMF in arbitrary space
dimensions is now equivalent to factorize all polynomial loops.
