Balanced multiwavelet bases based on symmetric FIR filters

This paper describes a basic difference between multiwavelets and scalar wavelets that explains, without using zero moment properties, why certain complications arise in the implementation of discrete multiwavelet transforms. Assuming we wish to avoid the use of prefilters in implementing the discrete multiwavelet transforms, it is suggested that the behavior of the iterated filter bank associated with a multiwavelet basis of multiplicity r is more fully revealed by an expanded set of r² scaling functions φ_i,j. This paper also introduces new K-balanced orthogonal multiwavelet bases based on symmetric FIR filters. The nonlinear design equations arising in this work are solved using the Grobner basis. The minimal-length K-balanced multiwavelet bases based on even-length symmetric FIR filters are better behaved than those based on odd-length symmetric FIR filters, as illustrated by special relations they satisfy and by examples constructed.