In a series of measurements, the sound power of 40 musical instruments, including all standard modern orchestral instruments, as well as some of their historic precursors from the classical and the baroque epoch, was determined using the enveloping surface method with a 32-channel spherical microphone array according to ISO 3745. Single notes were recorded at the extremes of the dynamic range (pp and ff) over the entire pitch range. In a subsequent audio content analysis, audio features were determined for all 3482 single notes using the timbre toolbox. In order to analyze the relative contributions of timbre- and amplitude-related properties to the expression of musical dynamics in different instruments, Bayesian linear discriminant analysis and generalized linear mixed modelling were employed to determine those audio features discriminating best between extremes of dynamics both within and across instruments. The results from these measurements and statistical analyses thus deliver a comprehensive picture of the acoustical manifestation of “musical dynamics” with respect to sound power and timbre for all standard orchestral instruments.

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.

Spherical harmonics representations are widely adopted in applications such as analysis, manipulation, and synthesis of wave fields that are either captured or simulated. Recent studies have shown that, for broadband fields, a time domain representation of spherical harmonics expansions can benefit from computational efficiency and favorable transient properties. For practical usage, an accurate discrete-time modeling of spherical harmonics expansions is indispensable. The main challenge is to model the so called radial functions which describe the radial and frequency dependencies. In homogeneous cases, they are commonly realized as finite impulse response filters where the coefficients are obtained by sampling the continuous-time representations. This article investigates the temporal and spectral properties of the resulting discrete-time radial functions. The spectral deviations caused by aliasing are evaluated both analytically and numerically, revealing the influence of the distance from the expansion center, sampling frequency, and fractional sample delay. It is also demonstrated how the aliasing distortion can be reduced by employing a recently introduced band limitation method.

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.