Motivated by the work of Frazier; and Gabardo and Nashed, we study \(P^{th}\)-stage nonuniform discrete wavelet frames (\(P^{th}\)-stage NUDW frames, in short) for \(\ell ^2(\Lambda )\), a nonuniform discrete space. In nonuniform discrete wavelet frames, the translation set is not necessary a group but a spectrum which is based on the theory of spectral pairs. We characterize first-stage nonuniform discrete Bessel sequences and wavelet frames in nonuniform discrete spaces. Duality and stability of first-stage NUDW frames are also discussed. Finally, by using first-stage NUDW frames, we provide a suitable way to construct the \(P^{th}\)-stage NUDW frames. We illustrate our construction with the help of a concrete example.

受Frazier工作的激励；以及Gabardo和Nashed，我们针对\（\ ell ^ 2（\ Lambda ）研究\（P ^ {th} \）级非均匀离散小波帧（简称为\（P ^ {th} \）级NUDW帧））\），一个不均匀的离散空间。在非均匀离散小波帧中，平移集不是必需的组，而是基于频谱对理论的频谱。我们表征了非均匀离散空间中的第一阶段非均匀离散贝塞尔序列和小波帧。还讨论了第一阶段NUDW帧的对偶性和稳定性。最后，通过使用第一阶段的NUDW帧，我们提供了一种合适的方式来构造\（P ^ {th} \）阶段的NUDW帧。我们将通过一个具体示例来说明我们的构造。