基于层的单纯拓扑上的拓扑IIR滤子
Topological IIR Filters over Simplicial Topologies via Sheaves
摘要：
拓扑学提供了一种方法，正式推广数字滤波方法的基础上，数字线性变换不变（LTI）的过滤器，同时，在原则上，结合变换变量和非线性方法，以及研究大规模（全球）的滤波器问题的属性。在这封信中，我们将展示如何LTI数字滤波器理论的全部内容可以纳入罗宾逊介绍的拓扑滤波器的形式主义。特别地，我们将给出与无限冲激响应（IIR）相关的反馈滤波器的构造。结果允许将LTI滤波器直接转化为拓扑滤波器，拓扑滤波器是有限向量空间的层和单纯拓扑上适当构造的线性映射。
英文摘要：
Topology offers a means to formally generalize digital filtering methods based on digital linear translation-invariant (LTI) filters while also, in principle, incorporating translation-variant and nonlinear methods as well as studying large scale (global) properties of filter problems. In this letter we show how the full content of LTI digital filter theory can be incorporated into the formalism of topological filters as introduced by Robinson. In particular, we will give the feedback filter construction associated with infinite impulse responses (IIR). The result allows for direct translation of LTI filters into topological filters, which are sheaves of finite vector spaces and suitably constructed linear maps over simplicial topologies.
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