On the applicability of the spherical wave expansion with a single origin for near-field acoustical holography

2013

A shotgun microphone is a highly directional pickup device widely used in noisy environments. The key element that leads to its superior directivity is a tube with multiple slot openings along its length. One traditional way to model the directional response of a shotgun is to assume plane waves traveling in the tube as if it is in the free field. However, the frequency response and directivity predicted by this traveling wave model can differ drastically from practical measurements. In this paper, an in-depth electroacoustic analysis was conducted to examine the problem by considering the standing waves inside the tube with an analogous circuit containing phased pressure sources and T-networks of tube segments. A further refinement is to model the housing diffraction effect with the aid of the equivalent source method (ESM). The on-axis frequency response and directivity pattern predicted by the proposed model are in close agreement with the measurements. From the results, a peculiar bifurcation phenomenon of directivity pattern at the Helmholtz frequency was also noted. While the shotgun behaves like an endfire array above the Helmholtz frequency, it becomes a broadside array below the Helmholtz frequency. The standing wave effect can be mitigated by covering the slot openings with mesh screen, which was found to alter the shotgun response to be closer to that of the traveling wave model above a critical frequency predicted by the half-wavelength rule. A mode-switching model was developed to predict the directional responses of mesh-treated shotguns.

Section: Modeling Diffraction Effects Of the Housingmentioning

confidence: 99%

Refined acoustic modeling and analysis of shotgun microphones

2013

“…We shall establish the acoustic system by using the ESM by which the sound field of interest is represented with an array of simple sources. [20][21][22][23] Two simple source models are introduced, including the plane-wave model and the spherical-wave model.…”

Section: A Finite Difference Approximationmentioning

confidence: 99%

“…A frequency-domain state-space model [17][18][19] is formulated in light of the equivalent source method (ESM). [20][21][22][23] The processing noise and measurement noise models are incorporated into the formulation. The unknown source amplitudes of the virtual sources are taken as the state variables to estimate.…”

Section: Introductionmentioning

confidence: 99%

Particle velocity estimation based on a two-microphone array and Kalman filter

Juan

Chen

2013

A traditional method to measure particle velocity is based on the finite difference (FD) approximation of pressure gradient by using a pair of well matched pressure microphones. This approach is known to be sensitive to sensor noise and mismatch. Recently, a double hot-wire sensor termed Microflown became available in light of micro-electro-mechanical system technology. This sensor eliminates the robustness issue of the conventional FD-based methods. In this paper, an alternative two-microphone approach termed the u-sensor is developed from the perspective of robust adaptive filtering. With two ordinary microphones, the proposed u-sensor does not require novel fabrication technology. In the method, plane wave and spherical wave models are employed in the formulation of a Kalman filter with process and measurement noise taken into account. Both numerical and experimental investigations were undertaken to validate the proposed u-sensor technique. The results have shown that the proposed approach attained better performance than the FD method, and comparable performance to a Microflown sensor.

“…While the ESM was often used as a benchmark for BEM, it has been shown with careful choice of parameters that the ESM is capable of achieving accuracy comparable to other methods. 15,23 Similar to IBEM, the use of ESM is not restricted to source with regular geometries. The simplicity of the ESM lends itself very well to the implementation with digital signal processing and control paradigms.…”

Section: Introductionmentioning

confidence: 99%

On optimal retreat distance for the equivalent source method-based nearfield acoustical holography

Chen

Lin

2011

As a basic form of the equivalent source method (ESM) that is used to nearfield acoustical holography (NAH) problems, discrete monopoles are utilized to represent the sound field of interest. When setting up the virtual source distribution, it is vital to maintain a "retreat distance" between the virtual sources and the actual source surface such that reconstruction would not suffer from singularity problems. However, one cannot increase the distance without bound because of the ill-posedness inherent in the reconstruction process with large distance. In prior research, 1-2 times lattice spacing, or the inter-element distance of microphones, is generally recommended as retreat distance in using the ESM-based NAH. While this rule has shown to yield good results in many cases, the optimal choice is a complicated issue that depends on frequency, geometry of the physical source, content of evanescent waves, distribution of sensors and virtual sources, etc. This paper deals about attaining the best compromise between the reconstruction errors induced by the point source singularity; the reconstruction ill-posedness is an interesting problem in its own right. The paper revisits this issue, with the aid of an optimization algorithm based on the golden section search and parabolic interpolation. Numerical simulations were conducted for a baffled planar piston source and a spherically baffled piston source. The results revealed that the retreat distance appropriate for the ESM ranged from 0.4 to 0.5 times the spacing for the planar piston, while from 0.8 to 1.7 times average spacing for the spherical piston. Experiments carried out for a vibrating aluminum plate also revealed that the retreat distance with 0.5 times the spacing yielded better reconstructed velocity than those with 1/20 and 1 times the spacing.