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. 2017 May;141(5):3220.
doi: 10.1121/1.4983093.

Sound-field measurement with moving microphones

Fabrice Katzberg  1 , Radoslaw Mazur  1 , Marco Maass  1 , Philipp Koch  1 , Alfred Mertins  1
Affiliations

Sound-field measurement with moving microphones

Fabrice Katzberg et al. J Acoust Soc Am. 2017 May.

Abstract

Closed-room scenarios are characterized by reverberation, which decreases the performance of applications such as hands-free teleconferencing and multichannel sound reproduction. However, exact knowledge of the sound field inside a volume of interest enables the compensation of room effects and allows for a performance improvement within a wide range of applications. The sampling of sound fields involves the measurement of spatially dependent room impulse responses, where the Nyquist-Shannon sampling theorem applies in the temporal and spatial domains. The spatial measurement often requires a huge number of sampling points and entails other difficulties, such as the need for exact calibration of a large number of microphones. In this paper, a method for measuring sound fields using moving microphones is presented. The number of microphones is customizable, allowing for a tradeoff between hardware effort and measurement time. The goal is to reconstruct room impulse responses on a regular grid from data acquired with microphones between grid positions, in general. For this, the sound field at equidistant positions is related to the measurements taken along the microphone trajectories via spatial interpolation. The benefits of using perfect sequences for excitation, a multigrid recovery, and the prospects for reconstruction by compressed sensing are presented.

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Figures

FIG. 1.
FIG. 1.
Arrangement of a virtual 2D sampling grid in space with reference to the grid coordinate system. The spatial sampling intervals Δx, Δy translate the discrete variables gx, gy to the world coordinate system. The dots represent the positions of the virtual grid RIRs. This example sketches one dynamic microphone moving along a Lissajous trajectory in between the grid positions.
FIG. 2.
FIG. 2.
Illustration of system matrices. (a) The system matrix A⌣ consisting of the column-wise concatenation of interpolation matrices Φu and (b) the system matrix A˜ consisting of shifted segments of Φu that allow for the decoupling of the time dimension.
FIG. 3.
FIG. 3.
Outline of multiresolution recovery. (a) The virtual grids g(v) in two-dimensional space and (b) the corresponding PAF subbands H(v)(k,ω) to be recovered.
FIG. 4.
FIG. 4.
Dynamic recovery on different virtual grids inside a constant plane using a Lissajous trajectory. Recovery quality of (a) the RIRs at the corners on the virtual grids and (b) the RIR at the center position on the virtual grids.
FIG. 5.
FIG. 5.
Comparison of recovery quality with and without multigrid approach for different interpolation methods and levels of measurement noise.
FIG. 6.
FIG. 6.
Frequency-dependent error with and without using the multigrid recovery scheme for different noise levels. (a), (b) SNR = 40 dB, (c), (d) SNR = 50 dB, and (e), (f) SNR = 60 dB. On the left-hand side, the linear interpolation was used, the right-hand side depicts the results of using the Lagrange interpolation.
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References

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