  We here use notions from the theory linear shift-invariant dynamical systems
to provide an easy-to-compute characterization of all rational wavelet filters.
For a given N bigger or equql to 2, the number of inputs, the construction is
based on a factorization to an elementary wavelet filter along with of m
elementary unitary matrices. We shall call this m the index of the filter. It
turns out that the resulting wavelet filter is of McMillan degree
$N((N-1)/2+m).
  Rational wavelet filters bounded at infinity, admit state space realization.
The above input-output parameterization is exploited for a step-by-step
construction (where in each the index m is increased by one) of state space
model of wavelet filters.
