Extending the bandwidth of an acoustic beamforming array using phase unwrapping and array interpolation

Abstract

A method is presented to suppress grating lobes in beamforming using phase unwrapping and array interpolation. When the phase of each cross spectrum is successfully unwrapped, the magnitude and phase of the cross spectral matrix may be interpolated; for cases where these quantities vary smoothly, interpolation is straightforward, even above the spatial Nyquist frequency. Two applications are presented: localization of a broadband source and characterization of a source with frequency-dependent location. In both cases, grating lobes are suppressed and the source is localized at frequencies up to at least 8 times the spatial Nyquist frequency.

Bias error analysis for phase and amplitude gradient estimation of acoustic intensity and specific acoustic impedance

“…Unwrapping can usually be successfully applied when the source is broadband with a smoothly varying phase and there is sufficient coherence between the microphones. 22,30 The PAGE bias error equations reported in Secs. III-V of this paper assume successful unwrapping.…”

Source characterization of full-scale tactical jet noise from phased-array measurements

“…In addition, the unwrapped-phase array interpolation (UPAINT) method-recently developed for interpolating levels and phase information along the measurement array-is applied to suppress adverse grating lobe effects and extend the usable frequency bandwidth beyond the spatial Nyquist frequency. 36,37 The HM-based source is used to compare the predicted sound pressure levels with those measured at various points in the mid field of the jet.…”

“…Where inverse and regularization methods are applied, these grating lobes may interfere with the estimation process by redistributing energy from the true source estimate location to the grating lobes, or vice versa. To ameliorate the source estimates, a method was developed by Goates et al 36 to increase the frequency bandwidth for the beamforming of broadband sources. A summary of the method is presented here, and a detailed description of the process is given in Ref.…”

“…A summary of the method is presented here, and a detailed description of the process is given in Ref. 36. This study represents the first application of the UPAINT method to jet noise source analysis.…”