Improved roundoff noise performance in a direct-form IIR filter using a modified delta operator

Abstract

Among various direct-form delta operator filters, the delta direct-form II transposed (/spl delta/DFIIt) has been shown to produce the lowest roundoff noise in finite-word-length 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/GDFIIt second-order section in which the /spl Delta/s at different branches are separately optimized to further suppress roundoff noise gain. Noise variance plots against pole locations are presented. Closed-form expressions for the optimal filter coefficients are derived and reduction of noise gain is confirmed by numerical examples.