BIBO stability of multidimensional filters with rational spectra

Classical conditions relating bounded input-bounded output (BIBO) stability to the behavior of the impulse response for one-dimensional discrete filters with rational spectra are reviewed and generalized to the multidimensional case. It is shown, in this manner, that these conditions are fundamentally predicated by rationality and not by the existence of isolated filter natural frequencies. Furthermore, the conditions are seen to lead to novel stability criteria applicable in the frequency-domain and minimum mean-square design of multi-dimensional filters.