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-based direct-form IIR filter with minimum roundoff noise gain and sensitivity. It utilizes the concept of different coupling coefficients at different branch nodes for better noise gain suppression. Two possible structures for realizing the inverse delta operator are considered and procedures for calculating the optimal filter coefficients are given. By means of state-space representation and matrix manipulation, it is also shown that expressions for sensitivity measures of different filter coefficients and their corresponding roundoff noise gain expressions are the same. This enables the simultaneous minimization of sensitivity and noise power for the proposed generalized filter structure.