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- Title
Parametrizations of All Wavelet Filters: Input-Output and State-Space.
- Authors
Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak
- Abstract
We here use notions from the theory linear shift-invariant dynamical systems to provide an explicit characterization, both practical and computable, of all rational wavelet filters. For a given N, (N ≥ 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. Moreover, beyond the parameters N and m, one confine the spectrum of the filters to lie in an open disk of radius ρ (stable filters mean ρ ∊ [0,1] and for FIR take ρ = 0). Then all filters can be described by a convex set of parameters ([0, π) × [0, 2π)2(N–1)× [0, ρ))m. Rational wavelet filters bounded at infinity, admit state space realization. The above input-output parametrization 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.
- Publication
Sampling Theory in Signal & Image Processing, 2013, Vol 12, Issue 2/3, p159
- ISSN
1530-6429
- Publication type
Article
- DOI
10.1007/BF03549566