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Least squares approach in wavenumber domain for sound field recording and reproduction using multiple parallel linear arrays

机译：波数域中的最小二乘法用于使用多个并行线性阵列进行声场记录和再现

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摘要

A novel signal processing method is proposed for sound field recording and reproduction using multiple parallel linear microphone and loudspeaker arrays. In sound field recording and reproduction, the problem is how to calculate the transfer filters that transform the signals recorded by microphones into the driving signals of the loudspeakers. The proposed method is based on the spatial Fourier transform in the horizontal angle combined with the least squares (LS) approach in the elevation angle. In the proposed method, the signals recorded by each linear microphone array and those that drive each loudspeaker array are decomposed into the wavenumber domain by the spatial Fourier transform in the horizontal direction. The transfer filters are then calculated by the LS approach in the wavenumber domain. As a result, the size of the matrix of each transfer function in the wavenumber domain is much smaller than that of the conventional LS approach in the temporal frequency domain (LSTF), and well-conditioned stable transfer filters can be obtained with low computational cost without regularization. Computer simulation results show that the proposed method reconstructed a sound field around the control points as accurately as the conventional LSTF.
机译：提出了一种使用多个平行线性麦克风和扬声器阵列进行声场记录和再现的信号处理方法。在声场记录和再现中，问题在于如何计算将麦克风记录的信号转换为扬声器的驱动信号的传递滤波器。所提出的方法是基于水平角的空间傅立叶变换和仰角的最小二乘（LS）方法相结合的。在所提出的方法中，通过水平方向上的空间傅立叶变换，将每个线性麦克风阵列记录的信号和驱动每个扬声器阵列的信号分解为波数域。然后通过LS方法在波数域中计算传递滤波器。结果，波数域中每个传递函数的矩阵大小比时频域（LSTF）中的常规LS方法小得多，并且可以以较低的计算成本获得条件良好的稳定传递滤波器没有正规化。计算机仿真结果表明，该方法与传统的LSTF一样准确地重建了控制点周围的声场。

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