Sound Field Reproduction Using Planar and Linear Arrays of Loudspeakers

Abstract

Abstract-In this paper, we consider physical reproduction of sound fields via planar and linear distributions of secondary sources (i.e., loudspeakers). The presented approach employs a formulation of the reproduction equation in spatial frequency domain which is explicitly solved for the secondary source driving signals. Wave field synthesis (WFS), the alternative formulation, can be shown to be equivalent under equal assumptions. Unlike the WFS formulation, the presented approach does not employ a far-field approximation when linear secondary source distributions are considered but provides exact results. We focus on the investigation of the spatial truncation and discretization of the secondary source distribution occurring in real-world implementations and present a rigorous analysis of evanescent and propagating components in the reproduced sound field.

An analytical approach to local sound field synthesis using linear arrays of loudspeakers

“…Further treatment shows that the synthesized sound field will generally only be correct on a line parallel to the x-axis at distance y = y ref [7]. At locations off this reference line, the synthesized sound field generally deviates from the desired sound field in terms of amplitude, propagation direction, and near-field components.…”

“…However, generally D(x, ω) will be dependent on the position of the receiver. This is mathematically reflected by the fact that y and z do not cancel out in (3) [7]. It is not surprising that we are not able to synthesize arbitrary sound fields since the secondary source setup is capable of creating wave fronts that propagate away from it.…”

“…We will treat this circumstance in an intuitive way in the following. Refer to [7] for a rigorous derivation.…”

“…For convenience, we illustrate the approach using the Spectral Division Method (SDM). The latter is available for planar and linear secondary source distributions [7]. Exemplarily, only linear distributions are treated in this paper.…”

Digital acoustics: processing wave fields in space and time using DSP tools

“…The second approach, known under the name of WFS [6], is based on the Huygens principle described in Section C. We note that we cannot do justice to a number of other approaches for reproducing sound fields. Some of them are extensions of WFS [36,37], some are based on multidimensional channel inversion [8], and there are many approaches based on matching spherical harmonic components between the desired and reproduced 3D sound fields [4,5,[38][39][40]]. …”