ABSTRACT
In this work, analytic expressions for the spatial coherence of noise fields are derived in the modal domain with the aim of providing a sparse representation. For this purpose, the sound field in a region of interest is expressed in terms of a given pressure distribution on a virtual surrounding cylindrical or spherical surface. According to the Huygens-Fresnel principle, the sound pressure on this surface is represented by a continuous distribution of elementary line or point sources, where orthogonal basis functions characterize the spatial properties. To describe spatially windowed pressure distributions with arbitrary angular extensions, orthogonal basis functions of limited angular support are proposed. As special cases, circular and spherical pressure distributions with uncorrelated source modes of equal power are investigated. It is shown that these distributions result, respectively, in cylindrically isotropic and spherically isotropic, i.e., diffuse noise fields. The analytic expressions derived in this work allow for a prediction of the spatial coherence between arbitrary positions within the region of interest, such that no microphones need to be placed at the actual points of interest. Simulation results are presented to validate the derived relations.
ABSTRACT
Spatial sound reproduction systems aim to produce a desired sound field over a volume of space. At high frequencies, the number of loudspeakers required is prohibitive. This paper shows that the use of loudspeakers with up to Nth order directivity allows reproduction over N times the bandwidth and produces a significantly attenuated exterior sound field. If the constraint on exterior cancellation of the field is removed, reproduction is possible over approximately 2N times the bandwidth. The use of higher order loudspeakers thus allows a significant reduction in the number of loudspeaker units, at the expense of increased complexity in each unit. For completeness, results are included for the generation of an exterior field with or without cancellation of the interior field.
ABSTRACT
Reproduction of a given sound field interior to a circular loudspeaker array without producing an undesirable exterior sound field is an unsolved problem over a broadband of frequencies. At low frequencies, by implementing the Kirchhoff-Helmholtz integral using a circular discrete array of line-source loudspeakers, a sound field can be recreated within the array and produce no exterior sound field, provided that the loudspeakers have azimuthal polar responses with variable first-order responses which are a combination of a two-dimensional (2D) monopole and a radially oriented 2D dipole. This paper examines the performance of circular discrete arrays of line-source loudspeakers which also include a tangential dipole, providing general variable-directivity responses in azimuth. It is shown that at low frequencies, the tangential dipoles are not required, but that near and above the Nyquist frequency, the tangential dipoles can both improve the interior accuracy and reduce the exterior sound field. The additional dipoles extend the useful range of the array by around an octave.
