Analysis of the effect of finite precision on the sigmoidal adaptive algorithm

This article proposes to analyze the performance of the Sigmoidal adaptive algorithm (SA) when implemented using fixed point arithmetic. In particuler, it provides the performance curve and mismatch, comparing them in different lengths of words (number of bits). The method presented in this paper propose a Taylor series approximation of the gradient of the cost function of the SA algorithm for finite precision implementation. It is shown that the algorithm presents stability for different lengths of words and that the increase in the level of the steady-state mismatch is sensitive or influenced by the quantization of the variables involved in the calculations.