Padois Thomas, Doutres Olivier, Sgard Franck
ETS, Montreal, QC, H3C 1K3, Canada.
IRSST, Montreal, QC, H3A 3C2, Canada.
J Acoust Soc Am. 2019 Mar;145(3):1546. doi: 10.1121/1.5094419.
The generalized cross correlation (GCC) is an efficient technique for performing acoustic imaging. However, it suffers from important limitations such as a large main lobe width for noise sources with low frequency content or a high amplitude of side lobes for noise sources with high frequencies. Prefiltering operation of the microphone signals by a weighting function can be used to improve the acoustic image. In this work, two weighting functions based on PHAse Transform (PHAT) improvements are used. The first adds an exponent to the PHAT expression (ρ-PHAT), while the second adds the minimum value of the coherence function to the denominator (ρ-PHAT-C). Numerical acoustic images obtained with the GCC and those weighting functions are compared and quantitatively assessed thanks to a metric based on a covariance ellipse, which surrounds either the main lobe or the side lobes. The weighting function ρ-PHAT-C provides the smallest surface ellipses especially when the arithmetic of the GCC is replaced by the geometric mean (GEO). Experimental measurements are carried out in a hemi-anechoic room and a reverberant chamber where two loudspeakers were set in front of microphone array. The acoustic images obtained confirm that the ρ-PHAT-C with the GEO outperforms the GCC, GCC-PHAT, and GCC ρ-PHAT.
广义互相关（GCC）是一种用于声学成像的有效技术。然而，它存在一些重要局限性，例如对于低频成分的噪声源，主瓣宽度较大；对于高频噪声源，旁瓣幅度较高。通过加权函数对麦克风信号进行预滤波操作可用于改善声学图像。在这项工作中，使用了基于相位变换（PHAT）改进的两种加权函数。第一种是在PHAT表达式中添加一个指数（ρ-PHAT），而第二种是在分母中添加相干函数的最小值（ρ-PHAT-C）。借助基于协方差椭圆的度量对使用GCC和这些加权函数获得的数值声学图像进行比较和定量评估，该协方差椭圆围绕主瓣或旁瓣。加权函数ρ-PHAT-C提供的椭圆面积最小，特别是当GCC的算法被几何均值（GEO）取代时。在半消声室和混响室中进行了实验测量，其中在麦克风阵列前设置了两个扬声器。获得的声学图像证实，采用GEO的ρ-PHAT-C优于GCC、GCC-PHAT和GCC ρ-PHAT。
