Direct form sensitivity reduction by order increase

The sensitivity of a Direct II form digital filter can be reduced by a factor of up to 10. This is achieved by providing additional degrees of freedom in the Direct II form by increasing the order. To maintain the original system function to be implemented, this corresponds to the addition of cancelling pole-zero pairs. The location of the latter influences the overall sensitivity function. As a measure of sensitivity the sum of L2norms of all first order partials of the system function is used. It is shown that this measure is particularly attractive because it can be evaluated efficiently and in closed form. This results from breaking down the sensitivity measure in terms of ARMA auto- and cross-covariances.