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.