Assessing the anisotropic features of spatial impulse responses
Résumé
The accurate spatial reproduction of sound is an important research area with applications in loudspeaker arrays as well as binaural headphones. Spherical harmonic decomposition techniques allow us to capture a sound field using a microphone array, store it, and reproduce it on various loudspeaker configurations. One challenge of spherical harmonic reproduction is using a smaller number of spherical harmonics on a larger loudspeaker array, where high coherence between loudspeakers can become an issue. Techniques such as Directional Audio Coding (DIRAC) aim to remedy this problem by analyzing the directionality of non-diffuse sounds and ensuring they are reproduced with high coherence while keeping the reverberant part spatially diffuse and incoherent. With these approaches, one key assumption is that the reverberant field can be reduced to a decorrelated but otherwise isotropic signal. Indeed, while the late reverberant part of an impulse response is considered diffuse due to high echo density in the temporal domain and high modal overlap in the frequency domain, the direction-dependent behavior of late reverberation now requires deeper study to reflect the increased spatial resolution of modern loudspeaker arrays. Recent studies have shown our capacity to detect small directional energy variations within the decay of noise signals, suggesting the need for more research to assess the perceptual threshold in the directivity of late reverberations. However, one key challenge in assessing this is measuring objectively the direction dependent features contained in a reverberant sound field. Towards this goal, this paper proposes a new approach to analyze, highlight and visualize the direction-dependent differences within the decay of spatial impulse responses. More specifically, this publication is proposing to combine and extend the use of existing methods used to analyze single channel room impulse responses to compare direction-dependent impulse responses. Indeed, by applying energy analysis methods such as the energy decay curves to directional impulse responses extracted through a beamforming method, we can obtain directional decay curves. These direction dependent curves can then be normalized, averaged and plotted to highlight non-isotropic features of a spatial impulse response. Furthermore, by normalizing the directional energy decay curves after the initial mixing time, we can study the energy decay deviation of specific directions. By highlighting the directions in which the directional decay differs from the mean decay, we aim to reveal the anisotropic features of the reverberation. The paper will cover various design choices offered by the method and how they impact the interpretation of the results. Recorded spatial impulses responses of different concert halls will be used to show practical examples of those design options. More specifically, we will demonstrate how the choice of a beamforming method can impact the resulting plots and their interpretation due to the width and amplitude of the main and side lobes of the beamformer. Filter banks can also be used to assess the frequency-direction dependent features of a spatial impulse response. Furthermore, normalization can be applied to focus the analysis method on directional decay deviation at different temporal stages. Through these different aspects, we will demonstrate how we can extract and visualize the anisotropy of a spatial impulse response. Ultimately, the proposed paper aims to contribute to the research field of multichannel reverberation reproduction and provides new objective measurement methods to establish the impact of anisotropic behavior in late reverberation. Being able to quantify and qualify directional features in late reverberant sound fields is an essential step in understanding how these features are perceived by human ears. BIBLIOGRAPHY: Berzborn, M. and Vorländer, M., “Investigations on the Directional Energy Decay Curves in Reverberation Rooms,” inProc. Euronoise 2018, pp. 2005–2010, Crete, Greece, 2018 Romblom, D., Guastavino, C., and Depalle, P., “Perceptual thresholds for non-ideal diffuse field reverberation,” The Journal of the Acoustical Society of America, 140(5), pp. 3908–3916, 2016, doi:10.1121/1.496752 Pulkki, “Spatial Sound Reproduction with Directional Audio Coding,” J. Audio Eng. Soc., vol. 55, no. 6, pp. 503–516 (2007 Jun.).[15] A. D. Pierce, “Concept of a Directional Spectral Energy Density in Room Acoustics,” J. Acoust. Soc. Am., vol. 56, no. 4, pp. 1304–1305 (1974 Oct.). C. G. Balachandran, D. W. Robinson, “Diffusion of the Decaying Sound Field,” Acta Acust., vol. 19, no. 5, pp.245–257 (1967 Jan.). D. Lubman, “Traversing Microphone Spectroscopy as a Means for Assessing Diffusion,” J. Acoust. Soc. Am., vol. 56, no. 4, pp. 1302–1304 (1974 Oct.).
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