Symbolic sensitivity analysis of IIR digital filters using MATLAB

摘要

This paper presents a MATLAB-based symbolic sensitivity analysis of second-order IIR digital filters. The sensitivity matrix of the pole displacement is derived in a symbolic form using the Symbolic Toolbox of MATLAB, and the symbolic expressions for various structures are presented. From the sensitivity matrix the variations of pole radius and angle are derived as a function of changes of the parameters of the denominator polynomial and the filter coefficients. In addition, a new second-order structure has been introduced and its pole sensitivities are compared with that of other known structures using the proposed sensitivity analysis.