Roundoff noise minimization in a modified direct-form delta operator IIR structure

Among various direct-form delta operator realized filter structures, the delta transposed direct-form II (delta DFIIt) has been shown to produce the lowest roundoff noise gain in finite wordlength implementations. Recent analyses focus on the optimization of the free parameter Delta of the delta operator, with scaling of the structure to prevent arithmetic overflow This paper proposes a modified delta DFIIt second-order section in which the Ps and filter coefficients at different branches are separately scaled to achieve improved roundoff noise gain minimization. Expressions For the filter coefficients are derived, and reduction of roundoff noise gain is verified by numerical examples.