The orthogonal interpolating balanced multiwavelet with rational coefficients

In this paper, we construct the orthogonal interpolating multiwavelet of multiplicity r=4r=4 with the balancing property of order 1 and with rational coefficients. At first, we introduce the notations of multiwavelet, interpolating and balancing. Secondly, for an orthogonal multiwavelet of multiplicity r=4r=4 having totally interpolating property, we deduce that the corresponding filter of the orthogonal multiscaling function with totally interpolating property has the parametric expression. Then, similarly to r=2r=2, we prove that there no exists any interpolating orthogonal multiwavelet with the symmetry. At last, we construct some examples of the orthogonal multiwavelets of multiplicity r=4r=4 with totally interpolating property and the balancing property of order 1 by the parametric way.