A time domain angular spectrum method is proposed to reconstruct nonstationary sound fields. In this method, the sound field is expressed as a superposition of a series of plane wave bases, and the plane wave basis is constructed by an impulse response function that relates the time domain angular spectrum to the field point pressure. The impulse response function consists of two parts, the propagating plane waves and the evanescent plane waves, and their physical interpretation is provided. By discretizing the time convolution between the plane wave strength and the impulse response function, the reconstruction can be carried out at each time step, thus providing the advantage of real-time reconstructing sound fields. Since the real-time reconstruction process is non-recursive, it can provide a stable reconstruction. In the reconstruction process, the Tikhonov regularization is introduced at each time step to obtain an appropriate estimation of the plane wave strength. Numerical simulations with an unsteady excitation plate and an experiment with an impacted plate were carried out to demonstrate the feasibility of the proposed method on reconstructing nonstationary sound fields. The effect of numerical parameters on the reconstruction accuracy was also investigated in the numerical simulations.

中文翻译：

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基于时域角谱法的非平稳声场重构

提出了一种时域角谱方法来重建非平稳声场。在这种方法中，声场表示为一系列平面波基的叠加，而平面波基是通过将时域角谱与场点压力相关的脉冲响应函数构造的。脉冲响应函数由传播平面波和the逝平面波两部分组成，并提供了它们的物理解释。通过离散化平面波强度和脉冲响应函数之间的时间卷积，可以在每个时间步长进行重构，从而提供了实时重构声场的优势。由于实时重建过程是非递归的，因此可以提供稳定的重建。在重建过程中 在每个时间步引入Tikhonov正则化，以获得对平面波强度的适当估计。进行了非稳态激励板的数值模拟和冲击板的实验，证明了该方法在重建非平稳声场中的可行性。数值模拟中还研究了数值参数对重建精度的影响。