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

Among various direct-form delta operator filters, the delta direct-form II transposed (δDFIIt) has been shown to produce the lowest roundoff noise in finite-word-length 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 δGDFIIt second-order section in which the Δs 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