Multi-channel spline adaptive filters for non-linear active noise control

This paper presents a non-linear multi-channel active noise control (ANC) scheme based on a set of adaptive spline filters as the component controllers. An adaptive spline filter comprises an adaptive finite impulse response (FIR) structure, which is followed by an adaptive spline activation function. A suitable learning rule is developed that updates the parameters of the adaptive FIR filter as well as of the adaptive spline function. Bounds on the learning rates for the proposed method are estimated and a detailed analysis on the computational complexity of the proposed scheme is presented. The proposed method is shown to offer good noise mitigation under non-linear ANC scenarios at a significantly lower computational load in comparison with other methods. In addition, due to the adaptive nature of the activation function, the proposed controller can transform itself from a non-linear to a linear one depending on the noise control scenario.