Efficient Synthesis of Room Acoustics via Scattering Delay Networks

An acoustic reverberator consisting of a network of delay lines connected via scattering junctions is proposed. All parameters of the reverberator are derived from physical properties of the enclosure it simulates. It allows for simulation of unequal and frequency-dependent wall absorption, as well as directional sources and microphones. The reverberator renders the first-order reflections exactly, while making progressively coarser approximations of higher-order reflections. The rate of energy decay is close to that obtained with the image method (IM) and consistent with the predictions of Sabine and Eyring equations. The time evolution of the normalized echo density, which was previously shown to be correlated with the perceived texture of reverberation, is also close to that of IM. However, its computational complexity is one to two orders of magnitude lower, comparable to the computational complexity of a feedback delay network (FDN), and its memory requirements are negligible

On the Convergence of the Multipole Expansion Method

The multipole expansion method (MEM) is a spatial discretization technique that is widely used in applications that feature scattering of waves from circular cylinders. Moreover, it also serves as a key component in several other numerical methods in which scattering computations involving arbitrarily shaped objects are accelerated by enclosing the objects in artificial cylinders. A fundamental question is that of how fast the approximation error of the MEM converges to zero as the truncation number goes to infinity. Despite the fact that the MEM was introduced in 1913, and has been in widespread usage as a numerical technique since as far back as 1955, to the best of the authors' knowledge, a precise characterization of the asymptotic rate of convergence of the MEM has not been obtained. In this work, we provide a resolution to this issue. While our focus in this paper is on the Dirichlet scattering problem, this is merely for convenience and our results actually establish convergence rates that hold for all MEM formulations irrespective of the specific boundary conditions or boundary integral equation solution representation chosen.Comment: 21 pages, 2 figures; Corrected a scaling error that occurred when plotting the third columns of Figs 1,2,3, some very minor grammatical edits to the intro/conclusion to improve clarity and conciseness, included funding info in first page; updated intro with historical info; reformatted several sections to reduce no. of pages; changed title, shortened abstract; fixed typo in proof of Thm 1.

Low-Complexity Steered Response Power Mapping based on Nyquist-Shannon Sampling

The steered response power (SRP) approach to acoustic source localization computes a map of the acoustic scene from the frequency-weighted output power of a beamformer steered towards a set of candidate locations. Equivalently, SRP may be expressed in terms of time-domain generalized cross-correlations (GCCs) at lags equal to the candidate locations' time-differences of arrival (TDOAs). Due to the dense grid of candidate locations, each of which requires inverse Fourier transform (IFT) evaluations, conventional SRP exhibits a high computational complexity. In this paper, we propose a low-complexity SRP approach based on Nyquist-Shannon sampling. Noting that on the one hand the range of possible TDOAs is physically bounded, while on the other hand the GCCs are bandlimited, we critically sample the GCCs around their TDOA interval and approximate the SRP map by interpolation. In usual setups, the number of sample points can be orders of magnitude less than the number of candidate locations and frequency bins, yielding a significant reduction of IFT computations at a limited interpolation cost. Simulations comparing the proposed approximation with conventional SRP indicate low approximation errors and equal localization performance. MATLAB and Python implementations are available online

Localization of a Virtual Wall by Means of Active Echolocation by Untrained Sighted Persons

The active sensing and perception of the environment by auditory means is typically known as echolocation and it can be acquired by humans, who can profit from it in the absence of vision. We investigated the ability of twentyone untrained sighted participants to use echolocation with self-generated oral clicks for aligning themselves within the horizontal plane towards a virtual wall, emulated with an acoustic virtual reality system, at distances between 1 and 32 m, in the absence of background noise and reverberation. Participants were able to detect the virtual wall on 61% of the trials, although with large di↵erences across individuals and distances. The use of louder and shorter clicks led to an increased performance, whereas the use of clicks with lower frequency content allowed for the use of interaural time di↵erences to improve the accuracy of reflection localization at very long distances. The distance of 2 m was the most difficult to detect and localize, whereas the furthest distances of 16 and 32 m were the easiest ones. Thus, echolocation may be used e↵ectively to identify large distant environmental landmarks such as buildings

Joint source localization and dereverberation by sound field interpolation using sparse regularization

In this paper, source localization and dereverberation are formulated jointly as an inverse problem. The inverse problem consists in the interpolation of the sound field measured by a set of microphones by matching the recorded sound pressure with that of a particular acoustic model. This model is based on a collection of equivalent sources creating either spherical or plane waves. In order to achieve meaningful results, spatial, spatio-temporal and spatio-spectral sparsity can be promoted in the signals originating from the equivalent sources. The inverse problem consists of a large-scale optimization problem that is solved using a first order matrix-free optimization algorithm. It is shown that once the equivalent source signals capable of effectively interpolating the sound field are obtained, they can be readily used to localize a speech sound source in terms of Direction of Arrival (DOA) and to perform dereverberation in a highly reverberant environment

Scattering Delay Network Simulator of Coupled Volume Acoustics

IEEEArtificial reverberators provide a computationally viable alternative to full-scale room acoustics simulation methods for deployment in interactive, immersive systems. Scattering delay network (SDN) is an artificial reverberator that allows direct parametric control over the geometry of a simulated cuboid enclosure as well as the directional characteristics of the simulated sound sources and microphones. This paper extends the concept of SDN reverberators to multiple enclosures coupled via an aperture. The extension allows independent control of the acoustical properties of the coupled enclosures and the size of the connecting aperture. The transfer function of the coupled-volume SDN system is derived. The effectiveness of the proposed method is evaluated in terms of rendered energy decay curves in comparison to full-scale ray-tracing models and scale model measurements

An automatic design procedure for low-order IIR parametric equalizers

Parametric equalization of an acoustic system aims to compensate for the deviations of its response from a desired target response using parametric digital filters. An optimization procedure is presented for the automatic design of a low-order equalizer using parametric infinite impulse response (IIR) filters, specifically second-order peaking filters and first-order shelving filters. The proposed procedure minimizes the sum of square errors (SSE) between the system and the target complex frequency responses, instead of the commonly used difference in magnitudes, and exploits a previously unexplored orthogonality property of one particular type of parametric filter. This brings a series of advantages over the state-of-the-art procedures, such as an improved mathematical tractability of the equalization problem, with the possibility of computing analytical expressions for the gradients, an improved initialization of the parameters, including the global gain of the equalizer, the incorporation of shelving filters in the optimization procedure, and a more accentuated focus on the equalization of the more perceptually relevant frequency peaks. Examples of loudspeaker and room equalization are provided, as well as a note about extending the procedure to multi-point equalization and transfer function modeling