Sensitivity Analysis for Normal and Canonical Internal Descriptions of a Notch Digital Filter

This paper analyzes coefficient sensitivity for the internal descriptions (state-space models) of a 2nd-order recursive notch digital filter. To this end, a 2nd-order recursive notch digital filter is realized by a normal-form or canonical-form internal description. The coefficient sensitivity for each internal description is then analyzed to derive the improved
$l_{2}$
-sensitivity measure. Moreover, the coefficient sensitivity of the normal-form internal description is compared with that of the canonical-form counterpart by means of numerical experiments. The simulation results clarify that the normal-form internal description has low coefficient sensitivity as a whole comparing to the canonical-form counterpart.