Mean square error analysis of nonuniform subband adaptive filters for system modeling

Nonuniform filterbanks have recently been proposed for subband adaptive filters (SAFs). However, nonuniform SAFs have not yet been given a thorough performance analysis. This paper gives a comprehensive mean square error (MSE) analysis of system modeling, nonuniform (and, degeneratively, uniform) SAFs after convergence for a specified filterbank. Using the equivalent polyphase representation suggested by Ono et al., minimum MSE (MMSE) estimates for the individual subband errors are presented with respect to a given filterbank for finite length (FIR), infinite length causal (IIR), and infinite noncausal adaptive filters. Using these subband MMSE estimators, an MMSE estimator is derived for the overall fullband error. Finally, the derived MMSE estimators are verified by a numerical simulation. The intent of this paper is not to compare nonuniform and uniform SAF performance but merely to present a unified mathematical methodology to predict their MMSEs.