Symmetric prefilters for multiwavelets

When applying discrete multiwavelets, prefiltering is necessary because the initial multiscaling coefficients cannot be trivially derived from the samples of scalar signals. The prefilters can be designed by using the superfunction theory. The idea is to construct a lowpass function from the multiscaling functions that inherits their approximation power for scalar signals. However, none of the existing prefilters give linear phase combined filters, which is important for many practical applications. In this paper, we analyze the conditions on which the prefilters and the combined filters are symmetric. We further propose a method to design good multiwavelet prefilters that allow the superfunction to be symmetric, satisfying the Strang-Fix conditions and the resulted combined filters are linear phase. We give a design example using the Chui-Lian multiwavelet.