  Orthogonal wavelets, or wavelet frames, for L^2(R) are associated with
quadrature mirror filters (QMF). The latter constitute a set of complex numbers
which relate the dyadic scaling of functions on R to the Z-translates, and
which satisfy the QMF-axioms. In this paper, we show that generically, the data
in the QMF-systems of wavelets is minimal, in the sense that it cannot be
nontrivially reduced. The minimality property is given a geometric formulation
in the Hilbert space l^2(Z), and it is then shown that minimality corresponds
to irreducibility of a wavelet representation of the algebra O_2; and so our
result is that this family of representations of O_2 on the Hilbert space
l^2(Z) is irreducible for a generic set of values of the parameters which label
the wavelet representations.
