An operator in signal flow graphs and its applications

In the theory of electrical networks, Tellegen´s theorem and its generalization play an important role. This theorem is a direct result of Kirchhoff´s laws. In a signal flow graph, the signals in the graph do not depend on Kirchhoff´s laws, and therefore Tellegen´s theorem does not apply to signal flow graphs. However, there exists a similar formula for signal flow graphs and digital filters. This formula is generalized by using the operator concept, and some of its applications are presented.<>