  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.
