The use of impulse response Grammians in the design of 2-D separable-denominator digital filters

A technique is developed for designing two-dimensional (2-D) separable-denominator digital filters in the spatial domain. The proposed technique utilizes the impulse response Grammians considered for 2-D separable-denominator digital filters. These Grammians are extensions of that proposed for single-input/single-output 1-D linear systems. The stability of the resulting filter is always guaranteed. Finally, an example is given to illustrate the use of the proposed technique