Abstract
An orthogonal scaling function ϕ(t) can realize perfect A/D (Analogue/Digital) and D/A if and only if ϕ(t) is cardinal in the case of scalar wavelet. But it is not true when it comes to multiwavelets. Even if a multiscaling function φ(t) is not cardinal, it also holds for perfect A/D and D/A. This property shows the limitation of Selesnick’s sampling theorem. In this paper, we present a general sampling theorem for multiwavelet subspaces by Zak transform and make a large family of multiwavelets with some good properties (orthogonality, compact support, symmetry, high approximation order, etc.), but not necessarily with cardinal property, realize perfect A/D and D/A. Moreover, Selesnick’s result is just the special case of our theorem. And our theorem is suitable for some symmetrical or nonorthogonal multiwavelets.
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