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

Abstract

Among various direct-form delta operator realized filter structures, the delta transposed direct-form II (/spl 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 /spl Delta/ of the delta operator, with scaling of the structure to prevent arithmetic overflow. This paper proposes a modified /spl delta/DFIIt second-order section in which the /spl Delta/s 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.