Construction of biorthogonal two-direction refinable function and two-direction wavelet with dilation factor mm

An algorithm for constructing a pair of biorthogonal two-direction refinable function and the corresponding biorthogonal two-direction wavelet is presented. In particular, the algorithm can also be used to construct two-direction orthogonal refinable function. Finally, we give an example illustrating how to use our method to construct biorthogonal two-direction scaling function with dilation factor 3.