We report the first systematic study of designed two-input biochemical systems as information processing gates with favorable noise transmission properties accomplished by modifying the gate's response from a convex shape to sigmoid in both inputs. This is realized by an added chemical "filter" process, which recycles some of the output back into one of the inputs. We study a system involving the biocatalytic function of the enzyme horseradish peroxidase, functioning as an AND gate. We consider modularity properties, such as the use of three different input chromogens that when oxidized yield signal detection outputs for various ranges of the primary input, hydrogen peroxide. We also examine possible uses of different filter effect chemicals (reducing agents) to induce the sigmoid response. A modeling approach is developed and applied to our data, allowing us to describe the enzymatic kinetics in the framework of a formulation suitable for evaluating the noise-handling properties of the studied systems as logic gates for information processing steps.