A new approach to the design of cost-optimal low-noise digital filters

An extension of the conventional state-space description is proposed in this paper for the representation of digital filters. In the proposed model, the future values of the internal variables depend not only on the present values but also on that of K- 1 previous time instants, where K is the order of the model. Expressions for the roundoff noise and the dynamic-range constraint have been obtained. Effects of structure transformation can be easily incorporated into these expressions. The optimum digital filter structure developed using the proposed model, in general, is computationally more efficient than that developed using the conventional state-space description. This paper proposes three different "noise-cost performance measures" which are indicative of the overall cost of the digital filter under a normed round-off noise. An illustrative example is included in the paper showing the improvement in the "noise-cost measure" by using the new model under each of the three different measures. Simulation of this example using the DINAP II has confirmed the theoretical results.