Multifilters and prefilters: Uniqueness and algorithmic aspects

In this paper we study the structure of prefilters which ensure a certain approximation order of a given multifilter system. We show how all prefilters can be obtained from the generic one and that in general these prefilters are necessarily rational filters, but point out how a judicious choice of parameters can be used to obtain FIR filters for the approximation orders 1 , 2 , 3 . Moreover, we illustrate the results by giving prefilters for the standard examples of multiwavelets.