A polyphase model for Fast Affine Projection with Partial Filter Update

In this paper, we propose a framework for analysing the convergence behavior of an affine projection based algorithm, using a polyphase filterbank model of the adaptive filter. We have recently introduced a low computation-cost version of the Fast Affine Projection Algorithm (FAPA) that combines FAPA with Partial Filter Update (PFU-FAPA). It is shown in this paper that the polyphase model of PFU-FAPA does not represent a perfect reconstruction system. This is in contrast to the sequential update LMS, which is based on a similar partial filter update method, and can be modeled by a perfect reconstruction polyphase filterbank. Hence, in PFU-FAPA, as the decimation rate of the partial update algorithm increases, distortion of the output signal increases. However, as the polyphase model shows, the distortion is only due to the effect of partial update on the autocorrelation estimation, and is negligible at low or modest decimation rates.