Active control of noise in a duct using the sparsely coded time-domain underdetermined multichannel inverse filters

A time-domain underdetermined multichannel inverse filtering (TUMIF) technique is proposed for active feedforward control of noise in ducts. Traditionally, feedforward active control is formulated as an overdetermined inverse filtering problem which generally leads to non-zero residual noise. In this work, a multichannel control approach is presented from the perspectives of vector subspaces and model-matching framework. By introducing multiple secondary sources, the problem can be reformulated into an underdetermined system, which admits infinite number of exact solutions with zero residual noise. However, the finite impulse response filter obtained using the least-square method tends to be prohibitively long for real-time implementation. To tackle this problem, two sparse coding techniques, the least absolute shrinkage and selection operator algorithm and the orthogonal matching pursuit algorithm, are exploited to reduce the controller orders. Simulation and experiment results obtained using a digital signal processor demonstrated that a two-channel reduced-order TUMIF controller has achieved significantly higher noise reduction than the filtered-x least-mean-squares algorithm.