Extension of the phase and amplitude gradient estimation method for acoustic intensity to narrowband sources

Abstract

The phase and amplitude gradient estimation (PAGE) method [D. C.Thomas et al., J. Acoust. Soc. Am. 137, 3366-3376 (2015)] has proven successful in improving the accuracy of measured energy quantities over the traditional p-p method in several applications. For example, the PAGE method has successfully increased the bandwidth over which magnitude and phase calculations are accurate for broadband sources with smoothly varying phase. This is partially accomplished by unwrapping the phase relationship in order to get valid phase information above the spatial Nyquist frequency. However, narrowband sources may not have sufficient coherent bandwidth information for a phase unwrapping algorithm to unwrap properly. To test the limits of the PAGE method on narrowband sources, sine waves, sawtooth waves, and bandlimited white noise have been used in various scenarios. In one-dimensional tests of these signals, the PAGE method provides correct magnitude and direction for frequencies up to the spatial Nyquist frequency, which represents an extended bandwidth over the p-p method. Additional specific results for the different input signals are presented. Also presented are the results of using low-level broadband noise propagating in the same general direction as the source to provide sufficient information for accurate phase unwrapping. [Work supported by NSF.]