Reconstruction of nonstationary sound fields based on the time domain plane wave superposition method.
Reconstruction of nonstationary sound fields based on the time domain plane wave superposition method.
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DOI：
10.1121/1.4746035
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发表时间：
2012-10
期刊：
影响因子：
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通讯作者：
Xiao-Zheng Zhang;Jean-Hugh Thomas;C. Bi;J. Pascal
中科院分区：
文献类型：
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作者：
Xiao-Zheng Zhang;Jean-Hugh Thomas;C. Bi;J. Pascal
提出了一种重建非平稳声场的时间域平面波叠加法。在该方法中，声场被表示为虚拟声源平面上估计的声压的时间波数谱与每个波数处的时间域传播核之间的时间卷积的叠加。通过直接对时间卷积进行离散化，可以在时间域内迭代进行重建，从而提供了连续重建随时间变化的压力信号的优势。在重建过程中，在每个时间步引入Tikhonov正则化，以获得虚拟源平面上的时间-波数谱的相关估计。由于该方法将二维空间傅里叶变换的双无限积分直接在波数域离散，因此不需要进行时域全息和实时近场声全息中常用的二维空间快速傅立叶变换，从而在理论上避免了与二维空间快速傅立叶变换相关的一些误差，并使非规则麦克风阵列的使用成为可能。数值仿真和两个说话人的实验验证了该方法的可行性。
A time-domain plane wave superposition method is proposed to reconstruct nonstationary sound fields. In this method, the sound field is expressed as a superposition of time convolutions between the estimated time-wavenumber spectrum of the sound pressure on a virtual source plane and the time-domain propagation kernel at each wavenumber. By discretizing the time convolutions directly, the reconstruction can be carried out iteratively in the time domain, thus providing the advantage of continuously reconstructing time-dependent pressure signals. In the reconstruction process, the Tikhonov regularization is introduced at each time step to obtain a relevant estimate of the time-wavenumber spectrum on the virtual source plane. Because the double infinite integral of the two-dimensional spatial Fourier transform is discretized directly in the wavenumber domain in the proposed method, it does not need to perform the two-dimensional spatial fast Fourier transform that is generally used in time domain holography and real-time near-field acoustic holography, and therefore it avoids some errors associated with the two-dimensional spatial fast Fourier transform in theory and makes possible to use an irregular microphone array. The feasibility of the proposed method is demonstrated by numerical simulations and an experiment with two speakers.