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An orthogonal scaling function (?)(t) can realize perfect A/D (Analogue/Digital) and D/A if and only if (?)(t) is cardinal in the case of scalar wavelet. But it is not true when it comes to multiwavelets. Even if a multiscaling function ?(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.
An orthogonal scaling function (?) (T) can realize perfect A / D (Analogue / Digital) and D / A if and only if (?) (T) is cardinal in the case of scalar wavelet. But it is not true when It comes to multiwavelets. Even if a multiscaling function? (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.