An efficient gradient-based iteration for direct form II sensitivity reduction

A reasonable coefficient sensitivity measure for state-space recursive, finite-wordlength, digital filters is the sum of the L ₂ norm of all first-order partials of the system function with respect to the system parameters. This measure is actually a lower bound approximation to the output quantization noise power. A gradient-based method for sensitivity minimization of direct-form II (infinite-impulse) filters is given. ARMA (autoregressive moving-average) sensitivity gradients are shown to consist also of ARMA auto- and cross-covariances, facilitating closed-form efficient evaluations. Some examples show the effectiveness of this procedure. The use of the design method in other filter forms is considered