The problem of acoustic noise is becoming increasingly serious with the growing use of industrial and medical equipment, appliances, and consumer electronics. Active noise control (ANC), based on the principle of superposition, was developed in the early 20th century to help reduce noise. However, ANC is still not widely used owing to the effectiveness of control algorithms, and to the physical and economical constraints of practical applications. In this paper, we briefly introduce some fundamental ANC algorithms and theoretical analyses, and focus on recent advances on signal processing algorithms, implementation techniques, challenges for innovative applications, and open issues for further research and development of ANC systems.

This paper describes a method to compute the far-field directivity of a parametric loudspeaker array (PLA), whereby the steerable parametric loudspeaker can be implemented when phased array techniques are applied. The convolution of the product directivity and the Westervelt's directivity is suggested, substituting for the past practice of using the product directivity only. Computed directivity of a PLA using the proposed convolution model achieves significant improvement in agreement to measured directivity at a negligible computational cost.

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The learning curves of the filtered-X least-mean-square (LMS) algorithm are theoretically obtained using a statistical-mechanics approach. The direction cosines among the vectors of an adaptive filter, its shifted filters, and an unknown system are treated as macroscopic variables. Assuming that the tapped-delay line is sufficiently long, simultaneous differential equations are obtained that describe the dynamical behaviours of the macroscopic variables in a deterministic form. The equations are solved analytically and show that the obtained theory quantitatively agrees with computer simulations. In the analysis, neither the independence assumption nor the few-taps assumption is used.