This paper is concerned with the mathematical analysis of experimental methods for the estimation of the power of an uncorrelated, extended aeroacoustic source from measurements of correlations of pressure fluctuations. We formulate a continuous, infinite dimensional model describing these experimental techniques based on the convected Helmholtz equation in $\mathbb{R}^3$ or $\mathbb{R}^2$. As a main result we prove that an unknown, compactly supported source power function is uniquely determined by idealized, noise-free correlation measurements. Our framework further allows for a precise characterization of state-of-the-art source reconstruction methods and their interrelations.

中文翻译：

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实验气动声学中逆源问题的唯一性

本文关注的是通过测量压力波动的相关性来估计不相关的扩展气动声源功率的实验方法的数学分析。我们基于 $\mathbb{R}^3$ 或 $\mathbb{R}^2$ 中的对流亥姆霍兹方程，制定了一个连续的无限维模型来描述这些实验技术。作为主要结果，我们证明了一个未知的、紧凑支持的源功率函数是由理想化的、无噪声的相关测量唯一确定的。我们的框架进一步允许精确表征最先进的源重建方法及其相互关系。