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 (δDFIIt) has been shown to produce the lowest roundoff noise gain in finite wordlength implementations. Recent analyses focus on the optimization of the free parameter Δ of the delta operator, with scaling of the structure to prevent arithmetic overflow. This paper proposes a modified δDFIIt second-order section in which the Δs 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