On the equivalence of spatial and temporal stability for translation invariant linear resistive networks

A fundamental relationship between spatial and temporal stability is explored for a class of translation-invariant linear resistive networks. These networks appear to have great promise for the high-speed linear filtering of two-dimensional spatially sampled analog data such as imagery. In general, networks designed for such applications require both positive and negative resistances. It is proved that such networks, when terminated in a certain reasonable manner, are temporally asymptotically stable in the presence of arbitrary parasitic capacitances whenever the network´s underlying spatial response (convolution) is bounded-input-bounded-output stable