Interpolatory Refinement is Low Pass Filtering

A new technique to analyse the convergence behavior of interpolatory refinement schemes is presented. The refinement schemes are considered as discrete low pass filters and the convergence analysis is done in the frequency domain. The class of subdivision schemes covered by this approach includes the stationary subdivision schemes but also a very general class of refinement schemes with global dependence of the new points form the old. The filter formalism can be used for both, the analysis and the construction of refinement schemes.