Abstract
A time-domain underdetermined multichannel inverse filtering technique is proposed for the feedforward active noise control (ANC) for ducts. In the commonly used filtered-x least-mean-square (FXLMS) algorithm, the feedforward control problem is formulated as an overdetermined inverse filtering problem which leads to non-zero residual noise. In the paper, a multichannel approach is derived in light of a vector subspace viewpoint and model-matching paradigm. By introducing multiple secondary sources, the problem can be reformulated into an underdetermined system, admitting infinite number of exact solutions with zero residual noise. However, as a major shortcoming of the approach, the resulting finite-length impulse response (FIR) filters tend to be too long to admit real-time implementation. To address the problem, the least absolute shrinkage and selection operator (LASSO) algorithm is exploited to effectively reduce the controller orders. Simulation and experiment results obtained for a two-channel duct ANC system have demonstrated the efficacy of the proposed approach in attenuating broadband noise.