Construction for biorthogonal interpolating scaling functions of multiplicity four

This paper focuses on the construction of biorthogonal interpolating multiscaling functions of multiplicity four with approximation order N. Firstly, using interpolating property, the parametric expression with filters of the biorthogonal multiscaling function is derived. Secondly, this paper also shows that there is not exist any interpolating biorthogonal multiwavelet of multiplicity 4 with symmetry. And theorem 2 described the relationship between dual filters of multiscaling functions. Then, the low-pass filters can be found by solving the equations generated by theorem 3.