论文标题
在声学中的线性离散逆问题中聚焦现象
Focusing Phenomena in Linear Discrete Inverse Problems in Acoustics
论文作者
论文摘要
线性离散反问题固有的焦点操作是形式化的。该开发是在声场繁殖的背景下给出的，其中源强度是在离散位置重新创建规定的压力场所需的逆解决方案。由于伪源固有的聚焦操作，系统的行为与每个控制点的声音串扰的量从根本上息息相关。串扰在仅一点点的最大化会导致系统中的线性依赖性。另一方面，它的最小化导致了理想的聚焦状态，其中源可以在每个点上选择性地聚焦，而在所有其他点都创建了零。提出了两个理论案例研究，这些案例研究表明了理想和超级理想的聚焦，其中后者的条件数是单一的。首先，检查了使用扬声器阵列的双耳音频复制的应用，并提出了几种理想聚焦的情况。在此过程中，最佳源分布是重新衍生的，并被证明是超级理想聚焦的情况。其次，使用统一线性阵列检查重新创建多个声音区域的应用。得出条件以在任意位于远场的控制点上实现理想的关注点。在所有情况下，保持理想聚焦作为频率函数的能力都需要对源或控制点几何形状的比例变化。
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.
