Adaptive filtering using constrained subband updates

This paper describes and analyzes a class of subband adaptive filters (SAFs) that stems from various approaches of applying subband and multirate techniques in adaptive filtering. This class of SAFs has a unique structure of weight-control mechanism where subband error signals are used to actuate the adaptation of a fullband weight vector. In this paper, we show that the recursive weight adaptation can be expressed as an underdetermined least-squares solution. Within this deterministic framework, we show its underlying affinity with the normalized least-mean-square (NLMS) and affine projection (AP) algorithms. We then compare the efficacy of these algorithms in terms of convergence rate and computational complexity.