Diffuse Sound Field Synthesis

Can uncorrelated surrounding sound sources be used to generate extended diffuse sound fields? By definition, targets are a constant sound pressure level, a vanishing average sound intensity, uncorrelated sound waves arriving isotropically from all directions. Does this require specific sources and geometries for surrounding 2D and 3D source layouts? As methods, we employ numeric simulations and undertake a series of calculations with uncorrelated circular/spherical source layouts, or such with infinite excess dimensions, and we point out relations to potential theory. Using a radial decay 1/r^b modified by the exponent b, the representation of the resulting fields with hypergeometric functions, Gegenbauer polynomials, and circular as well as spherical harmonics yields fruitful insights. In circular layouts, waves decaying by the exponent b=1/2 synthesize ideally extended, diffuse sound fields; spherical layouts do so with b=1. None of the layouts synthesizes a perfectly constant expected sound pressure level but its flatness is acceptable. Spherical t-designs describe optimal source layouts with well-described area of high diffuseness, and non-spherical, convex layouts can be improved by restoring isotropy or by mode matching for a maximally diffuse synthesis. Theory and simulation offer a basis for loudspeaker-based synthesis of diffuse sound fields and contribute physical reasons to recent psychoacoustic findings in spatial audio.

Ultraspherical/Gegenbauer polynomials to unify 2D/3D Ambisonic directivity designs

This report on axisymmetric ultraspherical/Gegenbauer polynomials and their use in Ambisonic directivity design in 2D and 3D presents an alternative mathematical formalism to what can be read in, e.g., my and Matthias Frank's book on Ambisonics or J\'er\^ome Daniel's thesis, Gary Elko's differential array book chapters, or Boaz Rafaely's spherical microphone array book. Ultraspherical/Gegenbauer polynomials are highly valuable when designing axisymmetric beams and understanding spherical t designs, and this report will shed some light on what circular, spherical, and ultraspherical axisymmetric polynomials are. While mathematically interesting by themselves already, they can be useful in spherical beamforming as described in the literature on spherical and differential microphone arrays. In this report, these ultraspherical/Gegenbauer polynomials will be used to uniformly derive for arbitrary dimensions D the various directivity designs or Ambisonic order weightings known from literature: max-DI/basic, max-rE , supercardioid, cardioid/inphase. Is there a way to relate higher-order cardioids and supercardioids? How could one define directivity patterns with an on-axis flatness constraint?

Theory and investigation of acoustic multiple-input multiple-output systems based on spherical arrays in a room

Spatial attributes of room acoustics have been widely studied using microphone and loudspeaker arrays. However, systems that combine both arrays, referred to as multiple-input multiple-output (MIMO) systems, have only been studied to a limited degree in this context. These systems can potentially provide a powerful tool for room acoustics analysis due to the ability to simultaneously control both arrays. This paper offers a theoretical framework for the spatial analysis of enclosed sound fields using a MIMO system comprising spherical loudspeaker and microphone arrays. A system transfer function is formulated in matrix form for free-field conditions, and its properties are studied using tools from linear algebra. The system is shown to have unit-rank, regardless of the array types, and its singular vectors are related to the directions of arrival and radiation at the microphone and loudspeaker arrays, respectively. The formulation is then generalized to apply to rooms, using an image source method. In this case, the rank of the system is related to the number of significant reflections. The paper ends with simulation studies, which support the developed theory, and with an extensive reflection analysis of a room impulse response, using the platform of a MIMO system.

Auralization based on multi-perspective ambisonic room impulse responses

Most often, virtual acoustic rendering employs real-time updated room acoustic simulations to accomplish auralization for a variable listener perspective. As an alternative, we propose and test a technique to interpolate room impulse responses, specifically Ambisonic room impulse responses (ARIRs) available at a grid of spatially distributed receiver perspectives, measured or simulated in a desired acoustic environment. In particular, we extrapolate a triplet of neighboring ARIRs to the variable listener perspective, preceding their linear interpolation. The extrapolation is achieved by decomposing each ARIR into localized sound events and re-assigning their direction, time, and level to what could be observed at the listener perspective, with as much temporal, directional, and perspective context as possible. We propose to undertake this decomposition in two levels: Peaks in the early ARIRs are decomposed into jointly localized sound events, based on time differences of arrival observed in either an ARIR triplet, or all ARIRs observing the direct sound. Sound events that could not be jointly localized are treated as residuals whose less precise localization utilizes direction-of-arrival detection and the estimated time of arrival. For the interpolated rendering, suitable parameter settings are found by evaluating the proposed method in a listening experiment, using both measured and simulated ARIR data sets, under static and time-varying conditions.

Perceptual evaluation of listener envelopment using spatial granular synthesis

Listener envelopment refers to the sensation of being surrounded by sound, either by multiple direct sound events or by a diffuse reverberant sound field. More recently, a specific attribute for the sensation of being covered by sound from elevated directions has been proposed by Sazdov et al. and was termed listener engulfment. This contribution investigates the effect of the temporal and directional density of sound events on listener envelopment and engulfment. A spatial granular synthesis technique is used to precisely control the temporal and directional density of sound events. Experimental results indicate that a directionally uniform distribution of sound events at time intervals $\Delta t < 20$ milliseconds is required to elicit a sensation of diffuse envelopment, whereas longer time intervals lead to localized auditory events. It shows that elevated loudspeaker layers do not increase envelopment, but contribute specifically to listener engulfment. Lowpass-filtered stimuli increase envelopment, but lead to a decreased control over engulfment. The results can be exploited in the technical design and creative application of spatial sound synthesis and reverberation algorithms.

The PerspectiveLiberator -- an upmixing 6DoF rendering plugin for single-perspective Ambisonic room impulse responses

Nowadays, virtual reality interfaces allow the user to change perspectives in six degrees of freedom (6DoF) virtually, and consistently with the visual part, the acoustic perspective needs to be updated interactively. Single-perspective rendering with dynamic head rotation already works quite reliably with upmixed first-order Ambisonic room impulse responses (ASDM, SIRR, etc.). This contribution presents a plugin to free the virtual perspective from the measured one by real-time perspective extrapolation: The PerspectiveLiberator. The plugin permits selecting between two different algorithms for directional resolution enhancement (ASDM, 4DE). And for its main task of convolution-based 6DoF rendering, the plugin detects and localizes prominent directional sound events in the early Ambisonic room impulse response and re-encodes them with direction, time of arrival, and level adapted to the variable perspective of the virtual listener. The diffuse residual is enhanced in directional resolution but remains unaffected by translatory movement to preserve as much of the original room impression as possible.