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We here use notions from the theory linear shift-invariant dynamical systemsto 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 isbased on a factorization to an elementary wavelet filter along with of melementary unitary matrices. We shall call this m the index of the filter. Itturns 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-stepconstruction (where in each the index m is increased by one) of state spacemodel of wavelet filters.

Easy-to-compute parameterizations of all wavelet filters: input-output and state-space