Learning in linear and nonlinear multirate digital systems by signal flow graphs

Learning in linear or nonlinear multirate systems is often a difficult task, especially for complex structures. Recently it has been shown that Signal Flow Graph (SFG) can be a very effective tool for adapting a huge variety of architecture, both linear and nonlinear, In this paper we show how it is possible to extend the use of the SFG approach also to multirate digital systems, linear and nonlinear. The proposed method is based on the concept of adjoint graph, which allows one to estimate the derivative of the output with respect to an internal parameter at different rates (time-instant). The new method can be employed for the gradient-based adaptation of general multirate circuits.