Performance of the phase and amplitude gradient estimator intensity method in interference fields

Abstract

The phase and gradient amplitude estimator (PAGE) method improves the frequency bandwidth of estimated acoustic intensity over the traditional p-p method without altering the spacing between microphones [D. C. Thomas et al., J. Acoust. Soc. Am. 137, 3366–3376 (2015)]. For many broadband sources, accurate estimates may be obtained beyond the spatial Nyquist frequency by unwrapping the phase of a transfer function used in obtaining the phase gradient. However, inaccurate phase unwrapping in interference fields, such as those produced by two loudspeakers with equal strengths but opposite phase, has been observed. This results in erroneous intensity vectors. A two-dimensional, multi-microphone intensity probe was employed to investigate this phenomenon. Findings include: (a) the unwrapping error does not occur for all interference nulls, but is more likely to occur for deeper interference nulls where there is reduction in coherence; (b) rotation of the probe in the field alters which pair-wise transfer function unwraps erroneously, but does not significantly alter the direction that contains the inaccurate intensity vectors; (c) removal of the interference nulls by driving the loudspeakers as incoherent sources allows for phase unwrapping to occur multiple times and accurate estimation of intensity vectors beyond 10 kHz. [Work supported by NSF.]