On the use of modified phase transform weighting functions for acoustic imaging with the generalized cross correlation
Thomas Padois, Olivier Doutres, Franck C. Sgard · The Journal of the Acoustical Society of America · 2019
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.