Optimal Dyadic Models of Time-Invariant Systems

The ease of simulating a dyadic model on digital computers suggests approximating linear time-invariant (LTI) systems by dyadic models. Methods for calculating the best such approximations are provided. It is shown that the matrices characterizing the LTI system and its optimal dyadic approximant have identical diagonal elements in the Walsh domain. This fact is used to derive a direct transformation between the impulse-response function of an LTI system and that of its dyadic approximant. The transformation can be accomplished in less than N log N additions.