Mixed time scale recursive algorithms

We investigate the behavior of certain types of mixed time scale adaptive algorithms. These systems comprise a “fast” or quickly changing algorithm mutually coupled to a “slow” or slowly changing algorithm. They arise naturally in a variety of adaptive environments such as in IIR system identification, the training of recurrent neural networks, decision feedback equalization, and others. [These algorithms (despite their title) should not be confused with the mixed time scales of wavelet transforms or other algorithms associated with multiresolution signal processing]. We give conditions for when the system can be analyzed from the framework of a simpler “frozen state” system. This analysis extends some of the previous work of Solo (1995) and his coworkers