A coefficient sensitivity bound in 2-D state-space digital filtering

For a SISO two-dimensional (2-D) state-space digital filter, a general upper bound on the sensitivity measurement of the filter's eigenfunctions is proposed. The bound for both equal and unequal word length registers of an optimal realization [11], [12] is calculated. It is shown that for a scaled equal wordlength realization, the bound has its minimum value.