Young-Seok CHOI †a) , Member SUMMARY A new type of the affine projection (AP) algorithms which incorporates the sparsity condition of a system is presented. To exploit the sparsity of the system, a weighted l 1 -norm regularization is imposed on the cost function of the AP algorithm. Minimizing the cost function with a subgradient calculus and choosing two distinct weightings for l 1 -norm, two stochastic gradient based sparsity regularized AP (SR-AP) algorithms are developed. Experimental results show that the SR-AP algorithms outperform the typical AP counterparts for identifying sparse systems. key words: system identification, adaptive filter, affine projection, sparsity, sparse system