Digital filter structures free of limit cycles

Abstract

In this paper recursive, second-order, digital filter-structures are given, that are free of zero input limit cycles. This holds for the two cases of sign-magnitude- and two's complement-truncation applied immediately after each multiplication. These structures provide for very inexpensive, but limit cycle free implementations of recursive, digital filters. The results, given for the case of zero input, are in a second part extended to the case of constant input by a simple, so called bypass-structure for the over-all transfer function.