Learning of periodic signals-an averaging analysis

This paper describes the concepts and background theory of the analysis of a neural-like network for the learning and replication of periodic signals containing a finite number of distinct frequency components. The approach is based on a two stage process consisting of a learning phase when the network is driven by the required signal followed by a replication phase where the network operates in an autonomous feedback mode while continuing to generate the required signal to a desired level of accuracy for a specified time. The analysis focusses on stability properties of a model reference adaptive control based learning scheme via the averaging method. The averaging analysis provides fast adaptive algorithms with proven convergence properties.