Digital Filter Designs that are Free of Limit Cycles

Abstract

Abstract : Finite word-length adders and quantizing methods used to construct digital filters can cause non-linearities to occur in the closed-loop filter system. Such nonlinearities can degrade system performance in what is known as a limit cycle behavior of the output. Overflow oscillations are limit cycles that are induced by the repeated overflow of finite word-length adders used in filter realizations. It is possible to construct digital filters that are free of overflow oscillations. Nonlinear analysis techniques can be used to derive conditions to govern digital filter designs that will be free of overflow oscillations. This paper will formulate a general theorem to ensure that nth order digital filters will be free of overflow oscillations. An implementation of digital filters with two's complement arithmetic adders is included to demonstrate the result of the analysis. Digital filters, Limit cycle behavior.