Multiwavelet prefilters. 1. Orthogonal prefilters preserving approximation order p⩽2

In applications using multiwavelets, there is a necessary step of associating a given discrete signal with a function in the scaling function space V₀. This association is equivalent to including a prefilter and a post-filter for the filter bank determined by the underlying multiwavelets. We give a construction for orthogonal (paraunitary) finite-impulse response (FIR) prefilters that preserve the approximation order of a given arbitrary scaling vector Ψ with approximation order p⩽2. We give several such prefilters for the DGHM multiwavelet