2011/05/02 by Daniel Alpay, Alpay, Daniel, Palle E. T. Jørgensen +3
Computer Science · Mathematics · #26C15 #42C40 #65T60 #93B15 #94C05 #Complex Variables (math.CV) #Digital Filter Design and Implementation #FOS: Electrical engineering #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1105.0256
openalex publication_date 2011/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.