Asymptotic behavior of nonlinear m-D digital filters with singularities on the distinguished boundary

The stability robustness of multidimensional digital filters with singularities on the distinguished boundary under the effect of finite wordlength is addressed. In particular, it is shown that all purely first-order digital filters with nonessential singularities of the second kind (NSSK) are asymptotically stable under certain types of nonlinearities. Even bounded-input bounded-output unstable multidimensional digital filters with singularities on the distinguished boundary are proved to be asymptotically stable in the first-order case. These results are then extended to certain classes of higher-order multidimensional digital filters. It is demonstrated that, although multidimensional digital filters with NSSKs on the distinguished boundary have no margin of linear stability, they might exhibit a rather robust behavior to nonideal effects such as finite wordlength