Abstract
Simplification of linear time-invariant discrete systems with stochastic noises is discussed. The “stochastic equivalence” is newly defined. Two systems are stochastically equivalent when their outputs have the same statistical properties in the steady state. The following three problems are considered: a) Find necessary and sufficient conditions for system equivalence. b) Obtain a simplifying procedure for finding one of those systems of simplest possible structure which are equivalent to a given system. c) Investigate how all these simplified systems are related with each other. The newly defined “minimum phase fundmental system” is shown to play an important role in this investigation.
