  This paper describes a novel technique for promoting sparsity in the modified
filtered-x algorithms required for active noise control. The proposed
algorithms are based on recent techniques incorporating approximations to the
\ell_0-norm in the cost functions that are used to derive adaptive filtering
algorithms. In particular, zero-attracting and reweighted zero-attracting
filtered-x adaptive algorithms are developed and considered for active noise
control problems. The results of simulations indicate that the proposed
techniques improve the convergence of the existing modified algorithm in the
case where the primary and secondary paths exhibit a degree of sparsity.
