Adjoint sensitivity models and signal-flowgraph reversal

The method of Seviora and Sablatash for obtaining adjoint digital filters is interpreted for general signal-flowgraph application. It is shown that the procedure reduces to the reversal operation for signal flowgraphs. Motivated by this result, a simple alternative derivation of the adjoint signal flowgraph is presented which is based on direct sensitivity models and Mason´s topological formula. Tellegen´s theorem or the calculus of variations are not required. The derivation is an extension to interreciprocal linear systems of an argument used by Leeds and Ugron for reciprocal networks.