Acoustic imaging using different weighting functions with the generalized cross correlation based on the generalized mean

The generalized cross correlation (GCC) is a standard technique for estimating time delay between microphone signals. A prefiltering operation by a weighting function may be included to whiten the cross spectrum of the microphones signals. The expected result is a narrow cross correlation function and a more accurate estimation of the time delay. Among the classic weighting functions, the most known is the PHAse Transform (PHAT). The ability of the PHAT weighting function to whiten the cross spectrum of the microphone signals can be improved by adding an exponent or the minimum value of the coherence function to the denominator. Both approaches have shown promising results for time delay estimation. In this work, the aforementioned modifications of the PHAT weighting function are considered for performing acoustic imaging with the classic GCC and the GCC based on the geometric mean. Numerical and experimental measurements are carried out in the case of two acoustic sources in front of a regular microphones array.