On the uniqueness of stationary points in L_2 approximation with a rational polyphase function

摘要

The question of uniqueness of L_2 approximation when using a rational polyphase function is of great importance for the practical use of polyphase IIR adaptive filters. As shown in a previous work, the polyphase structure can alleviate the problem of convergence speed in IIR adaptive filters, allowing their computational complexity gain over FIR adaptive filters to be exploited. In that work, however, a demonstration of a uniqueness property was not presented. In this paper, we initially present an example of a practical application and the gain in convergence speed that can be achieved by using a polyphase IIR adaptive filter.