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Mathematical Problems in Engineering
Volume 2013, Article ID 601623, 7 pages
Research Article

Subband Adaptive Filtering with -Norm Constraint for Sparse System Identification

Department of Electronic Engineering, Gangneung-Wonju National University, Gangneung 210-702, Republic of Korea

Received 27 September 2013; Revised 26 November 2013; Accepted 26 November 2013

Academic Editor: Yue Wu

Copyright © 2013 Young-Seok Choi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a new approach of the normalized subband adaptive filter (NSAF) which directly exploits the sparsity condition of an underlying system for sparse system identification. The proposed NSAF integrates a weighted -norm constraint into the cost function of the NSAF algorithm. To get the optimum solution of the weighted -norm regularized cost function, a subgradient calculus is employed, resulting in a stochastic gradient based update recursion of the weighted -norm regularized NSAF. The choice of distinct weighted -norm regularization leads to two versions of the -norm regularized NSAF. Numerical results clearly indicate the superior convergence of the -norm regularized NSAFs over the classical NSAF especially when identifying a sparse system.