Floating-point coefficient sensitivity and roundoff noise of recursive digital filters realized in ladder structures

Coefficient sensitivity and roundoff error with floating-point rounding have been investigated for several digital ladder filter structures. It is found that in all the cases studied, the ladder structures first proposed by Fettweis show a much lower coefficient sensitivity. In this paper, a hybrid cascade structure is proposed and synthesized. Its coefficient sensitivity is found to be between a conventional cascade structure and the ladder structures. Roundoff error is also investigated by extensive simulation. The new Fettweis ladder structure is found to exhibit the lowest roundoff error. This result is in agreement with the theoretical study which indicates that digital filters which exhibit reduced attenuation sensitivity tend to have less roundoff error.