A family of proportionate normalized subband adaptive filter algorithms.

*(English)*Zbl 1208.94026Summary: The concept of proportionate adaptation is extended to the normalized subband adaptive filter (NSAF), and seven proportionate normalized subband adaptive filter algorithms are established. The proposed algorithms are proportionate normalized subband adaptive filter (PNSAF), \(\mu \)-law PNSAF (MPNSAF), improved PNSAF (IPNSAF), the improved IPNSAF (IIPNSAF), the set-membership IPNSAF (SM-IPNSAF), the selective partial update IPNSAF (SPU-IPNSAF), and SM-SPU-IPNSAF which are suitable for sparse system identification in network echo cancellation. When the impulse response of the echo path is sparse, the PNSAF has initial faster convergence than NSAF but slows down dramatically after initial convergence. The MPNSAF algorithm has fast convergence speed during the whole adaptation. The IPNSAF algorithm is suitable for both sparse and dispersive impulse responses. The SM-IPNSAF exhibits good performance with significant reduction in the overall computational complexity compared with the ordinary IPNSAF. In SPU-IPNSAF, the filter coefficients are partially updated rather than the entire filter at every adaptation. In SM-SPU-IPNSAF algorithm, the concepts of SM and SPU are combined which leads to a reduction in computational complexity. The simulation results show good performance of the proposed algorithms.

##### MSC:

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |

93E11 | Filtering in stochastic control theory |

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\textit{M. Shams Esfand Abadi} and \textit{S. Kadkhodazadeh}, J. Franklin Inst. 348, No. 2, 212--238 (2011; Zbl 1208.94026)

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