Armlets and balanced multiwavelets: flipping filter construction

In the scalar-valued setting, it is well-known that the two-scale sequences {q/sub k/} of Daubechies orthogonal wavelets can be given explicitly by the two-scale sequences {p/sub k/} of their corresponding orthogonal scaling functions, such as q/sub k/=(-1)/sup k/p/sub 1-k/. However, due to the noncommutativity of matrix multiplication, there is little such development in the multiwavelet literature to express the two-scale matrix sequence {Q/sub k/} of an orthogonal multiwavelet in terms of the two-scale matrix sequence {P/sub k/} of its corresponding scaling function vector. This paper, in part, is devoted to this study for the setting of orthogonal multiwavelets of dimension r=2. In particular, the two lowpass filters are flipping filters, whereas the two highpass filters are linear phase. These results will be applied to constructing both a family of the most recently introduced notion of armlet of order n and a family of n-balanced orthogonal multiwavelets.