DESIGN CONSIDERATIONS AND STABILITY OF A DIGITAL-FILTER WITH FINITE WORD-LENGTH

A method to improve the stability of the forced response of a recursiv e digital filter with nonlinearities due to finite wordlength is prese nted. An analysis of applying a stability criterion on the nonlinear f ilter is performed by transforming the problem into a mathematical pro blem of finding a zero set. As a result of the mathematical analysis, one can find a maximal sector size that bounds an equivalent nonlinear ity, so that stability is ensured. This sector size is influenced by t he choice of the desired nonlinearity characteristic appropriate to th e problem, and the amount of the input scaling needed. Another improve ment of the filter's stability is obtained by adding a feedback gain, the value of which is determined by using the zero set-finding method. Simulation results showing the improved stability properties of a fil ter designed by this method are presented.