Sampling theory is one of the most powerful results in modern information theory and technology. The digital signal with sampling properties can be reconstructed from its samples in a perfect form. Walter and Zhou extended the Shannon sampling theorem to wavelet subspaces. This paper improves the classical sampling theorems based on wavelet frames. A basic problem on information theory is introduced here. For a given digital signal, whether it has sampling series form. In this paper, the digital signals with sampling properties are characterized based on wavelet frames. For a given sapling subspace, the analytic form of the signals in it is proposed. Especially some new kinds of sampling subspaces are offered here. As an application, the examples show that the new theorems improve some known relating results, which is effective for the digital signals’ sampling and reconstructions.