Abstract An interesting question about the perturbed sequences is: when do they inherit the properties of the original one? An elegant relation between frames (fusion frames) and their perturbations is the relation of their redundancies. In this paper, we investigate these relationships. Also, we express the redundancy of frames (fusion frames) in terms of the cosine angle between some subspaces.

中文翻译：

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帧和融合帧的扰动对其冗余的影响

摘要 关于扰动序列的一个有趣问题是：它们什么时候继承了原始序列的属性？帧（融合帧）与其扰动之间的一种优雅关系是它们的冗余关系。在本文中，我们研究了这些关系。此外，我们根据一些子空间之间的余弦角来表达帧（融合帧）的冗余。