There are two algorithms to solve the retarded time equation in the acoustic analogy. One is the classic retarded time method, and the other is the source time domain algorithm or the advanced time approach. The latter is more effective and simple than the former. However, difficulties may arise in the reconstruction of the acoustic signal in the observer time domain. The signal interpolation in every observer time step and a completeness check at the end are necessary for the reconstruction. In addition, two error regions which cannot to be ignored in frequency domain are generated by the latter. They are called the incomplete reception error. It is the main purpose of present work to analyze the formation process and characteristics of the incomplete reception error. Then the analysis is tested with a simplified model and the numerical results show that there are some spurious numerical oscillations in frequency domain if the incomplete reception regions are not removed. Finally, the difference between the method of directly removing the incomplete reception regions and the standard acoustic signal post-processing method is compared. The comparison results show that the method of removing incomplete reception regions directly is better.

中文翻译：

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声源时域积分算法中的不完全接收误差

在声学类比中，求解延迟时间方程有两种算法。一种是经典的延迟时间方法，另一种是源时域算法或高级时间方法。后者比前者更有效、更简单。然而，在观察者时域中重建声信号可能会出现困难。每个观察者时间步长的信号插值和最后的完整性检查对于重建是必要的。此外，后者产生了两个在频域中不可忽视的误差区域。它们被称为不完全接收错误。分析不完全接收错误的形成过程和特征是目前工作的主要目的。然后用简化模型对分析进行了测试，数值结果表明，如果不去除不完整的接收区域，频域中存在一些虚假的数值振荡。最后，比较了直接去除不完整接收区域的方法与标准声信号后处理方法的区别。对比结果表明，直接去除不完整接收区域的方法效果更好。