Spherical Harmonic Representation for Dynamic Sound-Field Measurements

Abstract

Continuously moving microphones produce a high number of spatially dense sound-field samples with low effort in hardware and acquisition time. By interpreting the dynamic procedure as the nonuniform sampling of spatial basis functions, a system of linear equations can be set up. Its solution encodes sound-field parameters that allow for the spatio-temporal reconstruction within the measurement area at bandwidths where static methods would require impractical setups. An existing framework considers such basis functions from a signal processing point of view. It uses sinc-function based interpolation filters which are highly localized around sampled trajectories and may lead to ill-posed problems unless sparsity constraints are made, especially for locations that are away from microphone trajectories. In this paper, we present a new physical interpretation of the dynamic sampling problem. Transferring the problem into frequency domain, we describe samples of a moving microphone in terms of sampled spherical harmonic functions. The use of these global basis functions leads to dynamic measurements that inherently encode expanded sound-field information and, thus, allow for robust reconstruction at off-trajectory positions.

Doppler frequency analysis for sound-field sampling with moving microphones

“…More recently, a new group of dynamic techniques have emerged, where the continuously acquired sound-field samples are directly embedded into a spatio-temporal context (Hahn and Spors, 2016;Katzberg et al, 2017bKatzberg et al, , 2018Katzberg et al, , 2021Hahn and Spors, 2018;Urbanietz and Enzner, 2020). Here, the measurement model is explicitly multidimensional, with a moving microphone that collects uniform samples in the time domain and, in general, nonuniform samples at varying points in the spatial domain.…”

“…Therefore, in (Katzberg et al, 2018;, a strategy has been proposed that exploits sparse Fourier representations and applies principles of compressed sensing (CS) (Candès et al, 2006). Recently, the dynamic framework subject to sinc-function related parameters has been generalized to a formulation, where arbitrary spatial basis functions cover expanded target volumes (Katzberg et al, 2021). Based on this, a physical perspective has been provided for representing dynamic sound-field samples in terms of spherical solutions to the acoustic wave equation (Katzberg et al, 2021).…”

Direction of arrival estimation using the rotating equatorial microphone

“…In fact, only limited research has been conducted on moving microphones as a whole. The few instances of study on moving microphones almost exclusively cover the measurement of room impulse responses either along the microphone trajectory, e.g., Ajdler et al (2007), Hahn and Spors (2015) and Hahn and Spors (2017), or in a given volume of interest using rapid microphone movement, e.g., Katzberg et al (2017) and Katzberg et al (2021). Since these approaches rely on known excitation signals for room impulse response measurement, they cannot be modified to allow for DOA estimation of unknown signals.…”

Comparison of Position Estimation Methods for the Rotating Equatorial Microphone

“…The authors of [6,7,8] target microphones that are moving rapidly in that the movement is so fast it introduces changes in the captured signal that are similarly fast, like those changes that are due to the time dependency of the source signal. These methods assume trajectories such as Lissajous figures that are difficult to implement in practice.…”

“…It is a rapid movement in that it occurs at speeds of up to a hundred rotations per second (RPS). The signals that are captured by this microphone can then be processed using, for example, a combination of the approaches from [8] and the EMA approach from [11] to obtain an orthogonal decomposition of the captured sound field based on which beamforming or other conventional processing methods can be applied. 978-1-6654-6867-1/22/$31.00 ©2022 IEEE c) reliable audio recording with a high sampling rate.…”