Using nonessential singularities of the second kind in two-dimensional filter design

It is shown that nonessential singularities of the second kind are not necessarily obstacles to the design of well-behaved (practical bounded-input/bounded-output (BIBO) stable) two-dimensional (2-D) discrete recursive filter transfer functions. For some widely utilized classes of filters, such as fan filters, it is shown that the existence of a nonessential singularity of the second kind on the unit bidisc is in fact required and, further, such filters, although BIBO unstable, can be designed to be practical-BIBO stable and well-behaved in practical applications.< >