线性离散声学反问题中的聚焦现象
Focusing Phenomena in Linear Discrete Inverse Problems in Acoustics
摘要：
形式化的线性离散反问题的固有的聚焦操作。发展的背景下，声场再现的源强度是需要重新创建一个规定的压力场在离散位置的逆解。系统的行为从根本上依赖于在每个控制点处的声学串扰的量，作为伪逆固有的聚焦操作的结果。仅在一个点处的串扰的最大化导致系统中的线性相关性。另一方面，它的最小化导致理想的聚焦状态，其中源可以选择性地聚焦在每个点处，而在所有其他点处创建空值。两个理论案例研究，演示理想和超理想聚焦，其中后者的条件数是单一的。首先，双耳音频再现使用扬声器阵列的应用程序进行检查，并提出了几种情况下的理想聚焦。在此过程中，最佳源分布被重新推导，并证明是一种情况下的超理想聚焦。其次，使用均匀线阵研究了重建多个声音区域的应用。导出了在远场任意位置的控制点处实现理想聚焦的条件。在所有情况下，保持作为频率的函数的理想聚焦的能力需要源或控制点几何形状的成比例变化。
英文摘要：
The focusing operation inherent to the linear discrete inverse problem is formalised. The development is given in the context of sound-field reproduction where the source strengths are the inverse solution needed to recreate a prescribed pressure field at discrete locations. The behaviour of the system is fundamentally tied to the amount of acoustic crosstalk at each control point as a result of the focusing operation inherent to the pseudoinverse. The maximisation of the crosstalk at just one point leads to linear dependence in the system. On the other hand, its minimisation leads to the ideal focusing state wherein the sources can selectively focus at each point, while a null is created at all other points. Two theoretical case studies are presented that demonstrate ideal and super ideal focusing, wherein the latter the condition number is unitary. First, the application of binaural audio reproduction using an array of loudspeakers is examined and several cases of ideal focusing are presented. In the process, the Optimal Source Distribution is re-derived and shown to be a case of super ideal focusing. Secondly, the application of recreating multiple sound zones is examined using a uniform linear array. The conditions are derived to achieve ideal focusing at control points positioned arbitrarily in the far-field. In all cases, the ability to maintain ideal focusing as a function of frequency requires proportional changes in the source or control point geometry.
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