State-Space Approaches for Model Reduction of FIR Digital Filters

In this paper, we review and compare three state-space methods for approximating a FIR digital filter by a reduced order IIR digital filter. The methods include the impulse-response gramians, the balanced model truncation, and the weighted least-squares approximation. The design steps for each of these methods and their results on three filter examples are presented. Results indicate that the performances of the balanced model truncation and the weighted least-square approximation are similar except the latter requires more computation; and both methods are able to yield better designs than those of the impulse-response gramians