Reduced sensitivities of direct form digital (sub) filter structures by increasing system order

A reasonable coefficient sensitivity measure for state-space recursive, finite-wordlength digital filters is the sum of the L/sub 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. The authors show that an important feature of this measure is that it can be broken down into evaluations of ARMA (autoregressive moving-average) auto-and cross-covariance sequences, all of which can be done efficiently and in closed form. The direct-form II sensitivity, which is shown to be approximately inversely proportional to the sum of products of system pole and zero distances, can usually be reduced by the judicious placement of added pole/zero cancellation pairs. These cancellation pairs provide extra degrees of freedom, which are used to minimize the sensitivity measure while not affecting the system function. The filter still has the direct-form II structure. A gradient-based method for sensitivity minimization is given. Some examples show its effectiveness.<
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