Sparse normalized subband adaptive filter algorithm with \(l_0\)-norm constraint.

*(English)*Zbl 1349.93385Summary: In order to improve the filters performance when identifying sparse system, this paper develops two sparse-aware algorithms by incorporating the \(l_0\)-norm constraint of the weight vector into the conventional Normalized Subband Adaptive Filter (NSAF) algorithm. The first algorithm is obtained from the principle of the minimum perturbation; and the second one is based on the gradient descent principle. The resulting algorithms have almost the same convergence and steady-state performance while the latter saves computational complexity. Whats more, the performance of both algorithms is analyzed by resorting to some assumptions commonly used in the analyses of adaptive algorithms. Simulation results in the context of sparse system identification not only demonstrate the effectiveness of the proposed algorithms, but also verify the theoretical analyses.

##### MSC:

93E11 | Filtering in stochastic control theory |

93E10 | Estimation and detection in stochastic control theory |

93E25 | Computational methods in stochastic control (MSC2010) |

93E12 | Identification in stochastic control theory |

##### Keywords:

identification; sparse system; normalized subband adaptive filter (NSAF); principle of the minimum perturbation; gradient descent principle
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\textit{Y. Yu} et al., J. Franklin Inst. 353, No. 18, 5121--5136 (2016; Zbl 1349.93385)

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