论文标题
拓扑拓扑的拓扑过滤器通过滑轮过滤
Topological IIR Filters over Simplicial Topologies via Sheaves
论文作者
论文摘要
拓扑提供了一种基于数字线性翻译不变（LTI）滤波器正式概括数字过滤方法的手段，同时还将结合翻译变体和非线性方法以及研究滤波器问题的大规模（全球）特性。在这封信中，我们展示了如何将LTI数字过滤器理论的全部内容纳入鲁滨逊介绍的拓扑过滤器的形式主义中。特别是，我们将提供与无限冲动响应（IIR）相关的反馈过滤器结构。结果允许将LTI过滤器直接转换为拓扑过滤器，这些拓扑过滤器是有限矢量空间的系带，并在简单拓扑的上适当地构造了线性图。
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.
