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Abstract: In this paper, we mainly pay attention to the weighted sampling and reconstruction algorithm in lattice-invariant signal spaces. We give the reconstruction formula in lattice-invariant signal spaces, which is a generalization of former results in shift-invariant signal spaces. That is, we generalize and improve Aldroubi, Gröchenig and Chen’s results, respectively. So we obtain a general reconstruction algorithm in lattice-invariant signal spaces, which the signal spaces is sufficiently large to accommodate a large number of possible models. They are maybe useful for signal processing and communication theory.

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