Notes on sampling theorem for multiwavelet

In the case of single wavelet, the orthogonal scaling function φ(t) can realize the perfect A/D and D/A if and only if it is cardinal. But it is not so in the case of multiwavelet. In our previous paper (Caiyan Jia and Xieping Gao 2002), we presented a general sampling theorem for multiwavelet subspaces, and gave some examples to point out that, though the multiwavelet has no cardinal property, it can also complete perfect A/D and D/A. In this note, we generalize the concept "general cardinal" to more general situation than in Caiyan Jia and Xieping Gao, and present a sufficient condition to realize perfect A/D and D/A for multiwavelet sampling.