A polyphase IIR adaptive filter

A polyphase structure for infinite-impulse response (IIR) adaptive filtering is proposed and compared to the direct structure in terms of their reduced error surface. It is shown that the general shape of its surface can make the polyphase structure have higher convergence speed, alleviating the problem of convergence speed in IIR adaptive filters and allowing their computational complexity gain over finite-impulse response (FIR) adaptive filters to be exploited. Benefits regarding filter stability are also achieved with the polyphase structure. An example of a high-speed digital subscriber line (HDSL) application is presented, for which the polyphase structure attains a gain of up to 70 times in convergence speed over an IIR direct structure, leading to roughly the same convergence speed of a FIR structure but with only 12% of its computational complexity. The question of uniqueness of the stationary points of the proposed structure is also discussed. It is pointed out that for white input and sufficient modeling, all stationary points are global minima, a result which does not follow directly from an equivalent property of the direct structure.