Easy-to-compute parameterizations of all wavelet filters: input-output and state-space Academic Article uri icon

abstract

  • Abstract: 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).

publication date

  • May 2, 2011