Stability analysis of digital filters under finite word-length effects

An approach is introduced for analysing the effects of finite word length and testing the stability in digital filters. Based on the analysis of both the quantisation errors of filter coefficients and the computational roundoff errors of multiplications and additions, a sufficient stability condition is introduced to give an insight into the hardware/cost tradeoff for word-length design choices under the effects of finite word length. The Bellman-Gronwall lemma in discrete form is employed to tackle this problem. In addition, some numerical examples are presented to illustrate the results.