We introduce a novel algorithm for the decomposition of a broadband soundfield into its component plane-waves. The algorithm, termed Sequential Direction Detection, decomposes the sound-field into L plane waves by recursively minimizing an objective function that determines the plane-wave directions, strengths and the number of plane-waves. The algorithm is described and tested on synthetic and real data. Extensions are discussed.

The nonuniform fast Fourier transform comprises a set of algorithms which approximately interpolate the usual discrete Fourier transform in the time and/or frequency domain. A nonuniform fast Fourier transform based on the fast multipole method was previously developed but passed over in favor of other approaches [1, 2]. This work extends a recent method for computing a periodized fast multipole method [3] with an adaptive algorithm that reduces the required number of multipole-to-local and local-to-local translations by an order of magnitude. This combination improves the speed and accuracy of the original algorithm, and results in an algorithm that is competitive with other nonuniform fast Fourier transforms. Numerical experiments are carried out comparing our implementation with others, demonstrating its viability.

Any acoustic sensor disturbs the spatial acoustic field to certain extent, and a recorded field is different from a field that would have existed if a sensor were absent. Recovery of the original (incident) field is a fundamental task in spatial audio. For some sensor geometries, the disturbance of the field by the sensor can be characterized analytically and its influence can be undone; however, for arbitrary-shaped sensor numerical methods have to be employed. In the current work, the sensor influence on the field is characterized using numerical (specifically, boundary-element) methods, and a framework to recover the incident field, either in the plane-wave or in the spherical wave function basis, is developed. Field recovery in terms of the spherical basis allows the generation of a higher-order Ambisonics representation of the spatial audio scene. Experimental results using a complex-shaped scatterer are presented.

We fundamentally reconsider implementation of the Fast Multipole Method (FMM) on a computing node with a heterogeneous CPU-GPU architecture with multicore CPU(s) and one or more GPU accelerators, as well as on an interconnected cluster of such nodes. The FMM is a divide-and-conquer algorithm that performs a fast N-body sum using a spatial decomposition and is often used in a time-stepping or iterative loop. Using the observation that the local summation and the analysis-based translation parts of the FMM are independent, we map these respectively to the GPUs and CPUs. Careful analysis of the FMM is performed to distribute work optimally between the multicore CPUs and the GPU accelerators. We first develop a single node version where the CPU part is parallelized using OpenMP and the GPU version via CUDA. New parallel algorithms for creating FMM data structures are presented together with load balancing strategies for the single node and distributed multiple-node versions. Our implementation can perform the N-body sum for 128M particles on 16 nodes in 4.23 seconds, a performance not achieved by others in the literature on such clusters.

Spherical and cylindrical microphone arrays offer a number of attractive properties such as direction-independent acoustic behavior and ability to reconstruct the sound field in the vicinity of the array. Beamforming and scene analysis for such arrays is typically done using sound field representation in terms of orthogonal basis functions (spherical/cylindrical harmonics). In this paper, an alternative sound field representation in terms of plane waves is described, and a method for estimating it directly from measurements at microphones is proposed. It is shown that representing a field as a collection of plane waves arriving from various directions simplifies source localization, beamforming, and spatial audio playback. A comparison of the new method with the well-known spherical harmonics based beamforming algorithm is done, and it is shown that both algorithms can be expressed in the same framework but with weights computed differently. It is also shown that the proposed method can be extended to cylindrical arrays. A number of features important for the design and operation of spherical microphone arrays in real applications are revealed. Results indicate that it is possible to reconstruct the sound scene up to order p with p2 microphones spherical array.

Spherical microphone arrays offer a number of attractive properties such as direction-independent acoustic behavior and ability to reconstruct the sound field in the vicinity of the array. Such ability is necessary in applications such as ambisonics and recreating auditory environment over headphones. We compare the performance of two scene reconstruction algorithms - one based on least-squares fitting the observed potentials and another based on computing the far-field signature function directly from the microphone measurements. A number of features important for the design and operation of spherical microphone arrays in real applications are revealed. Results indicate that it is possible to reconstruct the sound scene up to order p with p2microphones.

The numerical computation of head related transfer functions has been attempted by a number of researchers. However, the cost of the computations has meant that usually only low frequencies can be computed and further the computations take inordinately long times. Because of this, comparisons of the computations with measurements are also difficult. We present a fast multipole based iterative preconditioned Krylov solution of a boundary element formulation of the problem and use a new formulation that enables the reciprocity technique to be accurately employed. This allows the calculation to proceed for higher frequencies and larger discretizations. Preliminary results of the computations and of comparisons with measured HRTFs are presented.

Binaural presentation of X.Y sound is usually performed using virtual audio principles - that is, by attempting to virtually reproduce the setup of the X+Y loudspeakers in the reference room configuration. The computational cost of such playback is linear in the number of channels in the X.Y setup. We present a novel scheme that computes, offline, a spatio-temporal representation of the sound field in the listening area and store it as a multipole expansion. During head-tracked playback, the binaural signal is obtained by evaluating the multipole expansion at the ear position corresponding to the current user pose, resulting in a fixed playback cost. The representation is further extended to incorporate individualized HRTFs at no additional cost. Simulation results are presented.

Reverberation in rooms is often simulated with the image method due to Allen and Berkley (1979). This method has an asymptotic complexity that is cubic in terms of the simulated reverberation length. When employed in the frequency domain, it is relatively computationally expensive if there are many receivers in the room or if the source or receiver positions are changing with time. The computational complexity of the image method is due to the repeated summation of the fields generated by a large number of image sources. In this paper, a fast method to perform such summations is presented. The method is based on multipole expansion of the monopole source potential. For offline computation of the room transfer function for N image sources and M receiver points, use of the Allen-Berkley algorithm requires O(NM) operations, whereas use of the proposed method requires only O(N+M) operations, resulting in significantly faster computation of reverberant sound fields. The proposed method also has a considerable speed advantage in situations where the room transfer function must be rapidly updated online in response to source/receiver location changes. Simulation results are presented, and algorithm accuracy, speed, and implementation details are discussed. For problems that require frequency-domain computations, the algorithm is found to generate sound fields identical to the ones obtained with the frequency-domain version of the Allen-Berkley algorithm at a fraction of computational cost

We describe a new method for sound analysis using a spherical microphone array without the use of quadrature over the sphere. Quadrature based solutions are very sensitive to the placement of microphones on the sphere, needing measurements to be made at exactly the quadrature positions. We propose to use fitting with band-limited radial basis functions (RBFs) rather than quadrature. Our approach results in frequency independent beamformer weights for flexibly placed microphone locations. Results are demonstrated using both synthetic and real spherical array data.

The head related transfer function (HRTF) characterizes the scattering properties of a person's anatomy (especially the pinnae, head and torso), and exhibits considerable person-to-person variability. It is usually measured as a part of a tedious experiment, and this leads to the function being sampled at a few angular locations. When the HRTF is needed at intermediate angles, its value must be interpolated. Further, its range dependence is also neglected, which is invalid for nearby sources. Since the HRTF arises from a scattering process, it can be characterized as a solution of a scattering problem. In this paper, we show that by taking this viewpoint and performing some analysis we can express the HRTF in terms of a series of multipole solutions of the Helmholtz equation. This approach leads to a natural solution to the problem of HRTF interpolation. Furthermore, we show that the range-dependence of the HRTF in the near-field can also be obtained by extrapolation from measurements at one range.

Evaluating sums of multivariate Gaussians is a common computational task in computer vision and pattern recognition, including in the general and powerful kernel density estimation technique. The quadratic computational complexity of the summation is a significant barrier to the scalability of this algorithm to practical applications. The fast Gauss transform (FGT) has successfully accelerated the kernel density estimation to linear running time for low-dimensional problems. Unfortunately, the cost of a direct extension of the FGT to higher-dimensional problems grows exponentially with dimension, making it impractical for dimensions above 3. We develop an improved fast Gauss transform to efficiently estimate sums of Gaussians in higher dimensions, where a new multivariate expansion scheme and an adaptive space subdivision technique dramatically improve the performance. The improved FGT has been applied to the mean shift algorithm achieving linear computational complexity. Experimental results demonstrate the efficiency and effectiveness of our algorithm.

Understanding and simplified modeling of how humans generate cues from the scattering of sounds from their bodies holds the key to many applications in spatial audio. Scattering from the torso is thought to provide cues for source localization. A simplified two-sphere model has been proposed to understand the influence of the torso, and experimental studies have been performed. The availability of a validated numerical model can enable further parametric study and improved understanding using this model. Here we provide such a numerical model using the multipole method. Our method is validated by comparison with experimental data and commercial boundary element software. We find that most features of this “snowman” HRTF are reproduced by a simple model that places the “head” in the field of the source and the scattered field from the torso.

Understanding and simplified modeling of the head related transfer function (HRTF) holds the key to many applications in spatial audio. We develop an analytical solution to the problem of scattering of sound from a sphere in the vicinity of an infinite plane. Using this solution we study the influence of a nearby scattering rigid surface, on a spherical model for the HRTF.