Filippo Maria Fazi

Maximization of acoustic energy difference between two spaces

There has recently been an increasing interest in the generation of a sound field that is audible in one spatial region and inaudible in an adjacent region. The method proposed here ensures the control of the amplitude and phase of multiple acoustic sources in order to maximize the acoustic energy difference between two adjacent regions while also ensuring that evenly distributed source strengths are used. The performance of the method proposed is evaluated by computer simulations and experiments with real loudspeaker arrays in the shape of a circle and a sphere. The proposed method gives an improvement in the efficiency of radiation into the space in which the sound should be audible, while maintaining the acoustic pressure difference between two acoustic spaces. This is shown to give an improvement of performance compared to the contrast control method previously proposed.

Sound-field reproduction systems using fixed-directivity loudspeakers

Sound reproduction systems using open arrays of loudspeakers in rooms suffer from degradations due to room reflections. These reflections can be reduced using pre-compensation of the loudspeaker signals, but this requires calibration of the array in the room, and is processor-intensive. This paper examines 3D sound reproduction systems using spherical arrays of fixed-directivity loudspeakers which reduce the sound field radiated outside the array. A generalized form of the simple source formulation and a mode-matching solution are derived for the required loudspeaker weights. The exterior field is derived and expressions for the exterior power and direct to reverberant ratio are derived. The theoretical results and simulations confirm that minimum interference occurs for loudspeakers which have hyper-cardioid polar responses.

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.

An approach to generating two zones of silence with application to personal sound systems.

An application of current interest in sound reproduction systems is the creation of multizone sound fields which produce multiple independent sound fields for multiple listeners. The challenge in producing such sound fields is the avoidance of interference between sound zones, which is dependent on the geometry of the zone and the direction of arrival of the desired sound fields. This paper provides a theoretical basis for the generation of two zones based on the creation of sound fields with nulls and the positioning of those nulls at arbitrary positions. The nulls are created by suppressing low-order mode terms in the sound field expansion. Simulations are presented for the two-dimensional case which shows that suppression of interference is possible across a broad frequency audio range.

Sound reproduction systems using variable-directivity loudspeakers.

Sound reproduction systems using omnidirectional loudspeakers produce reflections from room surfaces which interfere with the desired sound field within the array. While active compensation systems can reduce the reverberant level, they require calibration in each room and are processor-intensive. Directional loudspeakers allow the direct to reverberant level to be improved within the array, but still produce a finite exterior field which reflects from the room surfaces. The use of variable-directivity loudspeakers allows the exterior field to be eliminated at low frequencies by implementing the Kirchhoff-Helmholtz integral equation. This paper investigates the performance of variable-directivity arrays in reducing reverberant levels and compares the results with those derived in a previous paper for fixed-directivity arrays. The results presented may have some impact on the design of commercial multi-channel systems for sound reproduction.

Generalized Sampling Expansion for Functions on the Sphere

Functions on the sphere appear in several applications, including geodesics, imaging and acoustics. Sampling of these functions may result in aliasing if the sampling condition is not met. The generalized sampling expansion introduced by Papoulis enables the reconstruction of a band-limited function sampled at a frequency lower than the Nyquist frequency using the outputs of several linear time-invariant systems. This paper formulates the generalized sampling expansion for functions on the sphere using spherical harmonics decomposition, facilitating sub-Nyquit sampling without aliasing error. An analysis of linear systems on the sphere and the aliasing phenomenon in the spherical harmonics domain is presented. Examples demonstrating the performance of the method and its limitations are studied.

Source splitting via the point source method

We introduce a new algorithm for source identification and field splitting based on the point source method (Potthast 1998 A point-source method for inverse acoustic and electromagnetic obstacle scattering problems IMA J. Appl. Math. 61 119–40, Potthast R 1996 A fast new method to solve inverse scattering problems Inverse Problems 12 731–42). The task is to separate the sound fields uj, j = 1, ..., n of n \in \mathbb {N} sound sources supported in different bounded domains G1, ..., Gn in \mathbb {R}^3 from measurements of the field on some microphone array—mathematically speaking from the knowledge of the sum of the fields u = u1 + sdotsdotsdot + un on some open subset ? of a plane. The main idea of the scheme is to calculate filter functions g_1, \ldots, g_n, n\in \mathbb {N} , to construct uell for ell = 1, ..., n from u|? in the form u_{\ell }(x) = \int _{\Lambda } g_{\ell,x}(y) u(y) {\,\rm d}s(y), \qquad \ell =1,\ldots, n. We will provide the complete mathematical theory for the field splitting via the point source method. In particular, we describe uniqueness, solvability of the problem and convergence and stability of the algorithm. In the second part we describe the practical realization of the splitting for real data measurements carried out at the Institute for Sound and Vibration Research at Southampton, UK. A practical demonstration of the original recording and the splitting results for real data is available online.

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.

3D soundfield reproduction using higher order loudspeakers

Three dimensional surround sound reproduction over large areas is a prevailing challenge due to the enormous numbers of loudspeakers required. In this paper, we propose an array of higher order loudspeakers which provide a mode matching solution to the problem based on 3D wavefield translation. It is shown that for a given bandwidth, the use of Lth order sources significantly brings down the minimum loudspeaker requirement by a factor of 1=(L + 1)2. Furthermore, the array is shown to be capable of exterior field cancellation, increasing its performance in echoing environments. Design examples are given for interior field, exterior field and interior and exterior combined field reproduction.

Sound field reproduction as an equivalent acoustical scattering problem

Given a continuous distribution of acoustic sources, the determination of the source strength that ensures the synthesis of a desired sound field is shown to be identical to the solution of an equivalent acoustic scattering problem. The paper begins with the presentation of the general theory that underpins sound field reproduction with secondary sources continuously arranged on the boundary of the reproduction region. The process of reproduction by a continuous source distribution is modeled by means of an integral operator (the single layer potential). It is then shown how the solution of the sound reproduction problem corresponds to that of an equivalent scattering problem. Analytical solutions are computed for two specific instances of this problem, involving, respectively, the use of a secondary source distribution in spherical and planar geometries. The results are shown to be the same as those obtained with analyses based on High Order Ambisonics and Wave Field Synthesis, respectively, thus bringing to light a fundamental analogy between these two methods of sound reproduction. Finally, it is shown how the physical optics (Kirchhoff) approximation enables the derivation of a high-frequency simplification for the problem under consideration, this in turn being related to the secondary source selection criterion reported in the literature on Wave Field Synthesis.