Sound field planarity characterized by superdirective beamforming

Abstract

The ability to replicate a plane wave represents an essential element of spatial sound field reproduction. In sound field synthesis, the desired field is often formulated as a plane wave and the error minimized; for other sound field control methods, the energy density or energy ratio is maximized. In all cases and further to the reproduction error, it is informative to characterize how planar the resultant sound field is. This paper presents a method for quantifying a region's acoustic planarity by superdirective beamforming with an array of microphones, which analyzes the azimuthal distribution of impinging waves and hence derives the planarity. Estimates are obtained for a variety of simulated sound field types, tested with respect to array orientation, wavenumber, and number of microphones. A range of microphone configurations is examined. Results are compared with delay-and-sum beamforming, which is equivalent to spatial Fourier decomposition. The superdirective beamformer provides better characterization of sound fields, and is effective with a moderate number of omni-directional microphones over a broad frequency range. Practical investigation of planarity estimation in real sound fields is needed to demonstrate its validity as a physical sound field evaluation measure. © 2013 Acoustical Society of America

Acoustic contrast, planarity and robustness of sound zone methods using a circular loudspeaker array

“…The planarity of the sound field-the extent to which the sound field in the bright zone resembles a plane waveis a physical measure recently proposed by Jackson et al (2013). The planarity metric is well suited to the situation considered here, where it is desirable to derive an objective measure of the sound field properties from the microphone array that is applicable even when a target sound field is not fully specified.…”

“…Here, as in Jackson et al (2013), a super-directive (contrast control) beamformer is used to determine the steering matrix weights. Finally, the planarity metric can be defined (for the bright zone) as the ratio between the energy due to the largest plane wave component and the total energy flux of plane wave components…”

Acoustic Imaging System Based on Digital MEMS Sensors

“…The system work as a beamforming [8] imaging system. Figure 7 show the image of the sound source at 5 kHz.…”

Personal audio with a planar bright zone

“…Planarity is a measure of the proportion of the energy in the bright zone that can be attributed to the direction of the principal energy component, 26 and is well suited to the situation considered here as it provides an objective measure of the spatial sound field properties without requiring a target field to be strictly defined. The energy distribution at the microphone array (over incoming plane wave direction) is given by w i ¼ ð1=2Þjw i j 2 , where w ¼ [w 1 , w 2 ,…,…”

“…II B) may optimize the listening experience without requiring explicit plane wave synthesis. 3,26 For single-zone reproduction, local approaches to plane wave synthesis have considered the manipulation of intensity 27 and the focusing of energy in the wavenumber domain. 28 The latter wavenumber domain point focusing (WDPF) approach does not require an estimate of the pressure gradient in the zone and may therefore be straightforwardly applied to a pressure microphone array, as adopted for existing multi-point sound zone approaches.…”