A generalized direct-form delta operator-based IIR filter with minimum noise gain and sensitivity

This brief presents the derivation of an arbitrary order delta operator-bas ed direct-form IIR filter with minimum roundoff noise gain and sensitivity. It utilizes the concept of different coupling coefficients at different br anch nodes for better noise gain suppression. Two possible structures for r ealizing the inverse delta operator are considered and procedures for calcu lating the optimal filter coefficients are given. By means of state-space r epresentation and matrix manipulation, it is also shown that expressions fo r sensitivity measures of different filter coefficients and their correspon ding roundoff noise gain expressions are the same, This enables the simulta neous minimization of sensitivity and noise power for the proposed generali zed filter structure.