Sensitivity analysis of digital filters using the continued fraction expansion

摘要

It is known that many structural schemes can be used to implement digital filters. Some structures of digital filters are characterized by low sensitivity of the characteristics to the accuracy of the representation of the coefficients. A separate group of methods for the structural synthesis of digital filters is based on the expansion of rational fractions, including transfer functions, into continued fractions. Because of this decomposition, ladder structures are obtained. The sensitivity of such ladder structures is analyzed in this paper. As a measure of the structure sensitivity, estimations of the partial derivatives of the transfer function coefficients with respect to the expansion coefficients in continued fraction were used. The analysis showed that the sensitivity of the transfer function coefficients to some expansion coefficients is very small. However, the presented examples show that the sensitivity to certain coefficients of expansion can exceed the sensitivity of the classical direct and the canonic forms.