A theoretical analysis of sound localisation, with application to amplitude panning

Below 700Hz sound fields can be approximated well over a region of space that encloses the human head, using the acoustic pressure and gradient. With this representation convenient expressions are found for the resulting Interaural Time Difference (ITD) and Interaural Level Difference (ILD). This formulation facilitates the investigation of various head-related phenomena of natural and synthesised fields. As an example, perceived image direction is related to head direction and the sound field description. This result is then applied to a general amplitude panning system, and can be used to create images that are stable with respect to head direction

Generation of half-space sound fields with application to personal sound systems

A method is presented for generating a sound field that is significantly attenuated over half of the reproduction region, which has application to the generation of two independent sound fields for two listeners. The half-space sound field is produced by attenuating the negative or positive modes in the cylindrical or spherical expansion of a plane wave or point source sound field. It is shown that this is equivalent to adding to the original sound field, in quadrature, a second field which is the Hilbert transform of the original field. The resulting analytic field has a small magnitude in one half of the plane. Methods are presented for controlling the attenuation in the unwanted half-space. Finally, a simulation is presented showing the generation of a wideband pulse that propagates across half of the area within a circular array of sources

Analysis and control of multi-zone sound field reproduction using modal-domain approach

Multi-zone sound control aims to reproduce multiple sound fields independently and simultaneously over different spatial regions within the same space. This paper investigates the multi-zone sound control problem formulated in the modal domain using the Lagrange cost function and provides a modal-domain analysis of the problem. The Lagrange cost function is formulated to represent a quadratic objective of reproducing a desired sound field within the bright zone and with constraints on sound energy in the dark zone and global region. A fundamental problem in multi-zone reproduction is interzone sound interference, where based on the geometry of the sound zones and the desired sound field within the bright zone the achievable reproduction performance is limited. The modal-domain Lagrangian solution demonstrates the intrinsic ill-posedness of the problem, based on which a parameter, the coefficient of realisability, is developed to evaluate the reproduction limitation. The proposed reproduction method is based on controlling the interference between sound zones and sound leakage outside the sound zones, resulting in a suitable compromise between good bright zone performance and satisfactory dark zone performance. The performance of the proposed design is demonstrated through numerical simulations of two-zone reproduction in free-field and in reverberant environments

Evaluation of ambisonics decoding methods with experimental measurements

Ambisonics is a sound reproduction technique based on the decomposition of the sound field using spherical harmonics. The truncation in the number of coefficients used to recreate the sound field leads to reproduction artifacts which depend on the frequency and the listener spatial location. In this work, the performance of three different decoding methods (Basic, Max-rE and In-Phase) has been studied and evaluated in the light of the results of experimental measurements. The latter were performed using a spherical array composed of 40 uniformly distributed loudspeakers and a translating 29-channel linear microphone array. An error analysis is presented based on the difference between the desired and synthesized sound pressure and acoustic intensity field. The results indicate that, as expected, the size of the region of accurate sound field reconstruction reduces as frequency increases, but with different trends depending on the type of decoder implemente

Measuring spatial impulse responses in concert halls and opera houses employing a spherical microphone array

Traditional methods for measuring impulse responses in rooms provide detailed time and frequency resolution, but very poor spatial information. On the other hand, when a disturbing echo or discrete reflection is found, it would be very useful to be able to understand its exact direction-of-arrival. And detailed spatial information is also required when the measured impulse responses are employed as digital filters for virtual listening tests.The method described here is based on the usage of a small spherical microphone array, equipped with 32 subminiature capsules (Knowles Electronics) mounted flush on the surface of a rigid sphere (70mm diameter). A set of 32x25 digital FIR filters are employed for processing the signals coming from the capsules, and deriving the 25 channels corresponding to a spherical harmonics decomposition of the sound field, up to 4th order. Proper postprocessing tools allow for plotting the spatial information contained in the measured set of 25 impulse responses, making it easy to visualize the spatial distribution of sound during the propagation.This set can also be employed inside a special listening room, equipped with a spherical array of loudspeakers, for reconstruction faithfully the original soundfield, providing a realistic and immersive listening experience

Nonuniqueness of the solution of the sound field reproduction problem with boundary pressure control

This paper studies the circumstances under which the problem of reproducing a desired sound field using the boundary pressure control approach has a unique solution. The sound field reproduction problem is formulated as an inverse problem, in which the reproduction of the target sound field is attempted in the interior of a bounded control region surrounded by a continuous distribution of secondary sources. The determination of the secondary source strength is an ill-posed problem. A general formula for the solution is derived (assuming its existence) and it is shown that nonuniqueness arises when the wavenumber is one of the Dirichlet eigenvalues of the control region. It is shown that, when this is not the case, the solution of the problem is unique. Some strategies are presented that enable the nonuniqueness to be overcome. The case is also studied of the wavenumber being one of the Dirichlet eigenvalues of the region bounded by the secondary source distribution, which contains but generally does not coincide with the control region. The results derived are illustrated for a two dimensional problem with a finite number of secondary sources

The relationship between sound field reproduction and Near-Field Acoustical Holography

The problem of reproducing a desired sound field with an array of loudspeakers and the technique known as Near-Field Acoustical Holography share some fundamental theoretical aspects. It is shown that both problems can be formulated in terms of an integral equation which usually defines an ill-posed problem. The example of spherical geometry is discussed in detail. It is shown that for both the reproduction and the acoustical holography cases, the ill-conditioning of the problem is greatly affected by the distance between the source layer and the measurement/control surface.</p

Sound field reproduction using directional loudspeakers and the equivalent acoustic scattering problem

ABSTRACT The problem is addressed of reproducing a desired sound field in the interior of a bounded region of space, using an array of loudspeakers that exhibit a first order acoustic radiation pattern. Previous work has shown that the computation of the required loudspeaker signals, in the case of omnidirectional transducers, can be determined by solving an equivalent scattering problem. This approach is extended here to the case of directional loudspeakers. It is shown that the loudspeaker complex coefficients can be computed by solving an equivalent scattering problem. These coefficients are given by the normal derivative of the total pressure field (incident field plus scattered field) arising from the scattering of the target field by an object with the shape of the reproduction region (the region bounded by the loudspeaker array) and with impedance boundary conditions. The expression for this impedance, or Robin, boundary condition is calculated from the radiation pattern of the loudspeakers, assuming that the latter can be expressed by a linear combination of a free field Green function and its gradient. The solution of the problem can be obtained in closed form for simple geometries of the loudspeaker array, such as a sphere, a circle or a plane, thus providing a meaningful improvement to sound field reproduction techniques such as Wave Field Synthesis or High Order Ambisonics. The method proposed is also valid for more general geometries, for which the computation of the solution should be performed by applying the Kirchhoff approximation or by means of numerical methods

A multi-channel audio system based on the theory of integral equations

The basics of a multi-channel audio system, which attempts the reproduction of a desired sound field, are presented. The system's hardware consists of a three-dimensional array of loudspeakers, and can be used in combination with a specially designed microphone array. The mathematical fundamentals on which this technique is grounded consist of the formulation of the problems as an integral equation. The loudspeaker signals are determined from the knowledge of the target sound field on the boundary of a given control volume. The solution to this inverse problem is computed performing a singular value decomposition of the integral operator involved. For some simple array geometries it is possible to calculate an analytical solution to the problem. A regularization method is applied, as required by the ill-posed nature of the inverse problem under consideration. Some insight into the physical meaning of the ill-posedness is given and some analogies to Near-field Acoustic Holography are suggested. The effectiveness of the method proposed has been verified experimentally and some of the experimental results are presented. Finally, it is shown how this technique has been successfully applied to the design of a multi-channel auralisation system for room acoustics