Generalized subband decomposition adaptive filters for sparse systems

Abstract

Transform domain adaptive filtering algorithms can provide significant improvement in the convergence rate of time domain adaptive filters such as the least-mean-square (LMS) algorithm for coloured input signals. For sparse systems, the convergence rate can be further increased if the active region of the system response is identified. A number of fast-converging time domain adaptive filtering algorithms have been developed in the past for sparse systems. Because sparse systems in the time domain do not necessarily translate into sparse systems in the transform domain, fast-converging time domain algorithms cannot be applied to transform domain algorithms directly. In this paper we show that if a generalized subband decomposition structure is employed, the sparsity of the system response can be preserved in the transform domain. A fast-converging algorithm based on the proportionate normalized LMS algorithm is developed for generalized subband decomposition and its effectiveness is demonstrated in computer simulations.