Mixed time scale recursive algorithms

In this paper, we investigate the behavior of certain types of mixed time s cale adaptive algorithms. These systems comprise a "fast" or quickly changi ng algorithm mutually coupled to a "slow" or slowly changing algorithm, The y arise naturally in a variety of adaptive environments such as in IIR syst em identification, the training of recurrent neural networks, decision feed back equalization, and others. [These algorithms (despite their title) shou ld not be confused with the mixed time scales of wavelet transforms or othe r algorithms associated with multiresolution signal processing.] We give co nditions for when the system can be analyzed from the framework of a simple r "frozen state" system, This analysis extends some of the previous work of Solo and his coworkers.