Spatial-domain design of overflow-stable 2-D digital filters

In this paper, we present a constrained optimization design procedure for local state-space (LSS) two-dimensional (2-D) digital filters. The designed filter is guaranteed to be free of oscillations due to the overflow nonlinearity. This approach eliminates the need for first finding the LSS realization from the transfer function and then applying transformations to obtain an overflow-stable realization. It is shown that for the general second-order LSS filter, the constraint does not limit the flexibility of the design. An example to illustrate this approach is also given.