Construction of a class of compactly supported symmetric and balanced refinable function vector by GTST

The concept of general two-scale similarity transform (GTST) is introduced. By applying GTST, we present an algorithm of constructing a class of balanced refinable function vector by balancing already existing nonbalanced refinable function vector. In addition, we discuss an especial setting. That is, if given refinable function vector Φ(x) is symmetric, then by GTST, new refinable function vector Ψ(x) is not only balanced but also preserve symmetry. Finally, two construction examples are given.