A coherence-based phase and amplitude gradient estimator method for calculating active acoustic intensity

The phase and amplitude gradient estimator (PAGE) method [Thomas, Christensen, and Gee, J. Acoust. Soc. Am. 137, 3366-3376 (2015)] has been developed as an alternative to the traditional p-p method for calculating energy-based acoustic measures such as active acoustic intensity. While this method shows many marked improvements over the traditional method, such as a wider valid frequency bandwidth for broadband sources, contaminating noise can lead to inaccurate results. Contaminating noise degrades performance for both the traditional and PAGE methods and causes probe microphone pairs to exhibit low coherence. When coherence is low, better estimates of the pressure magnitude and gradient can be obtained by using a coherence-based approach, which yields a more accurate intensity estimate. This coherence-based approach to the PAGE method, known as the CPAGE method, employs two main coherence-based adjustments. The pressure magnitude adjustment mitigates the negative impact of uncorrelated contaminating noise and improves intensity magnitude calculation. The phase gradient adjustment uses coherence as a weighting to calculate the phase gradient for the probe and improves primarily the calculation of intensity direction. Though requiring a greater computation time than the PAGE method, the CPAGE method is shown to improve intensity calculations, both in magnitude and direction.