Wave Field Synthesis allows the reconstruction of an arbitrary target sound field within a listening area by using a secondary source contour of spherical monopoles. While phase correct synthesis is ensured over the whole listening area, amplitude deviations are present besides a predefined reference curve. So far, the existence and potential shapes of this reference curve was not extensively discussed in the Wave Field Synthesis literature. This article introduces improved driving functions for 2.5D Wave Field Synthesis. The novel driving functions allow for the control of the locations of amplitude correct synthesis for arbitrarily shaped—possibly curved—secondary source distributions. This is achieved by deriving an expressive physical interpretation of the stationary phase approximation leading to the presented unified Wave Field Synthesis framework. The improved solutions are better suited for practical applications. Additionally, a consistent classification of existing implicit and explicit 2.5D sound field synthesis solutions as special cases of the unified framework is given.

The avoidance of spatial aliasing is a major challenge in the practical implementation of sound field synthesis. Such methods aim at a physically accurate reconstruction of a desired sound field inside a target region using a finite ensemble of loudspeakers. In the past, different theoretical treatises of the inherent spatial sampling process led to anti-aliasing criteria for simple loudspeaker array arrangements, e.g., lines and circles, and fundamental sound fields, e.g., plane and spherical waves. Many criteria were independent of the listener's position inside the target region. Within this paper, a geometrical framework based on ray-approximation of the underlying synthesis problem is proposed. Unlike former approaches, this model predicts spatial aliasing artefacts for arbitrary convex loudspeaker arrays and as a function of the listening position and the desired sound field. Anti-aliasing criteria for distinct listening positions and extended listening areas are formulated based on the established predictions. For validation, the model is applied to different analytical sound field synthesis approaches: The predicted spatial structure of the spatial aliasing agrees with numerical simulation of the synthesised sound fields. Moreover, it is shown within this framework, that the active prioritization of a control region using so-called local sound field synthesis approaches does indeed reduce spatial aliasing artefacts. For the scenario under investigation, a method for local wave field synthesis achieves an artefact-free synthesis up to a frequency which is between 2.9 and 17.3 times as high as for conventional wave field synthesis.

Sound field synthesis aims at the reproduction of an arbitrary target sound field over an extended listening area applying a densely spaced loudspeaker ensemble. Two basic analytic methodologies—the explicit and the implicit—exist in order to derive the required loudspeaker driving functions. The explicit solution aims at the direct solution of the involved integral equation describing the general sound field synthesis problem, resulting in driving functions in the form of a spectral integral. The implicit solution extracts the driving function from an appropriate boundary integral representation of the target sound field. So far the relationship between two approaches was investigated for target field specific synthesis scenarios. For linear arrays this paper introduces a high-frequency approximation for the explicit solution resulting in a novel, purely spatial domain formulation of the direct approach. The presented driving functions allow the synthesis of an arbitrary virtual sound field, optimizing the reproduction on an arbitrary reference line. It is furthermore shown that for an arbitrary virtual sound field, the implicit solution constitutes a high-frequency approximation of the explicit method.

The sound field synthesis of moving sound sources is of great importance when dynamic virtual sound scenes are to be reconstructed. Previous solutions considered only virtual sources moving uniformly along a straight trajectory, synthesized employing a linear loudspeaker array. This article presents the synthesis of point sources following an arbitrary trajectory. Under high-frequency assumptions 2.5D Wave Field Synthesis driving functions are derived for arbitrary shaped secondary source contours by adapting the stationary phase approximation to the dynamic description of sources in motion. It is explained how a referencing function should be chosen in order to optimize the amplitude of synthesis on an arbitrary receiver curve. Finally, a finite difference implementation scheme is considered, making the presented approach suitable for real-time applications.

Wave Field Synthesis (WFS) is a spatial audio rendering technique that aims to reconstruct a desired sound field using dense arrays of secondary loudspeakers. WFS can theoretically produce realistic wavefronts over an extended area. However, practical implementations suffer from fundamental limitations. These include amplitude errors away from the reference listening region, diffraction artifacts caused by the finite array aperture, loss of low-frequency content due to high-frequency assumptions in the driving signals, and aliasing artifacts from the discretization of the secondary source array. In this paper, we present a rigorous analysis on the amplitude errors and diffractional effects by asymptotically evaluating the integral expressions underlying WFS. The resulting expressions reveal how the reproduced sound field can be decomposed into an ideal target component and additional diffraction terms that account for truncation and other boundary effects. We illustrate the impact of these effects on amplitude accuracy for typical secondary source distributions (linear and circular arrays) and extend the analysis to focused sources (virtual sources placed inside the loudspeaker array).

This paper establishes explicit low-frequency validity limits for 2.5D Wave Field Synthesis (WFS) derived from the Kirchhoff approximation. We show that the breakdown at low frequencies is governed by the applicability of the stationary phase approximation to the 2.5D Kirchhoff integral. This is quantified via an effective window (aperture) length that compresses the influence of secondary loudspeaker array size, tapering, referencing, and source/receiver proximity into a single quantity. We derive closed-form cutoff conditions for arbitrary source models and listening positions, yielding a cutoff wavenumber that scales with the inverse square of the effective length and recovers classical Fresnel-number/zone theory in frontal directions. The analysis predicts markedly higher cutoff for lateral positions and for sources/receivers near the SSD, and quantifies the impact of tapering and referencing schemes. Simulations with linear and circular loudspeaker arrays for plane, point, and focused sources validate the theory, including the intermediate transition band bounded by the two asymmetric effective lengths.