Realization of 2-D state-space filters with fewer multipliers

The authors illustrate that, under certain controllability and observability conditions on the one-dimensional block diagonal subsystems, they can considerably reduce the number of multipliers required for hardware implementation of two-dimensional filters. Although these conditions require some additional properties from the filter parameters, the saving in cost of hardware realization is judged to be well worth the extra effort to verify initially whether these conditions are met. A systematic procedure for obtaining the coefficients of a minimal number of multipliers, when the filter satisfies the proposed conditions, is presented. A numerical example is considered to illustrate the accuracy of the proposed technique