Manifold learning for global active noise control: Sensor interpolation

Abstract

To achieve global control, unmeasured frequency responses (FRs) of a control source and preselected control points are required. In this paper, sensor interpolation (SI) approaches based on plane wave decomposition (PWD), kernel ridge regression, deep neural network (DNN) are presented. A broadened control region encompassing a large number of measured and fictitious control points can be obtained using the SI techniques. PWD is a two-stage procedure that begins with trimming down plane wave components, followed by an extraction of the associated complex amplitudes. In kernel ridge regression, a reproducing kernel in the Hilbert space (RKHS) is utilized to interpolate continuous relative transfer functions. The DNN-based SI approach is inspired by the kernel method. Convolutional neural networks and the like are exploited to interpolate the FRs at the fictitious points. Simulations are conducted for a thirty-microphone uniform linear array. From the results, an excellent fit between the FRs at the fictitious points and the ground truth generated by the image source method can be obtained below the spatial aliasing frequency. The efficacy of the interpolated FRs in relation to global control is demonstrated via an example of feedforward active noise control using a linear loudspeaker array.