Finite word-length effects in m-D digital filters with singularities on the stability boundary

The author addresses stability robustness with respect to finite word-length conditions for multidimensional (m-D) digital filters with singularities on the distinguished boundary. In particular, it is shown that all purely first-order digital filters with nonessential singularities of the second kind (NSSKs) are asymptotically stable under certain types of nonlinearities. Even bounded-input, bounded-output (BIBO)-unstable m-D digital filters with singularities on the distinguished boundary proved to be asymptotically stable in the first-order case. The results are then extended to certain classes of higher-order m-D digital filters. It is demonstrated that, although linear m-D digital filters with NSSKs on the distinguished boundary have no margin of stability in the l₁, l₂ or asymptotic sense, they might exhibit a rather robust asymptotic behavior with respect to nonideal effects such as finite word-length conditions