Broadband multizone sound rendering by jointly optimizing the sound pressure and particle velocity

Abstract

In this paper, a recently proposed approach to multizone sound field synthesis, referred to as joint pressure and velocity matching (JPVM), is investigated analytically using a spherical harmonics representation of the sound field. The approach is motivated by the Kirchhoff-Helmholtz integral equation and aims at controlling the sound field inside the local listening zones by evoking the sound pressure and particle velocity on surrounding contours. Based on the findings of the modal analysis, an improved version of JPVM is proposed, which provides both better performance and lower complexity. In particular, it is shown analytically that the optimization of the tangential component of the particle velocity vector, as is done in the original JPVM approach, is very susceptible to errors and thus not pursued anymore. Furthermore, the analysis provides fundamental insights as to how the spherical harmonics used to describe three-dimensional sound fields translate into two-dimensional basis functions as observed on the contours surrounding the zones. By means of simulations, it is verified that discarding the tangential component of the particle velocity vector ultimately leads to an improved performance. Finally, the impact of sensor noise on the reproduction performance is assessed.

Time-Domain Sound Field Reproduction with Pressure and Particle Velocity Jointly Controlled

“…While the joint control of sound pressure and particle velocity for sound field reproduction is especially suited to non-uniform loudspeaker array setup with reduce number of loudspeakers and control points required, the proposed time-domain reproduction method has the potential to be used in real-time applications. However, for long-length RIRs and control filters, the inverse solution in (16) requires very high computational complexity. To solve this problem, the eigenvalue decomposition (EVD) based approach is adopted with the conjugate gradient (CG) method to search for the optimal solution in an iterative manner.…”

“…While most existing work focuses on controlling sound pressure only, some recent work started to investigate controlling the particle velocity in sound field reproduction [14]. A joint control of sound pressure and particle velocity has also been proposed for singlezone [15] and multi-zone sound field reproduction [16]. A general finding is that particle velocity assisted sound field reproduction is especially suitable to a non-uniformly spaced loudspeaker array with reduced number of loudspeakers and control points required.…”

Intensity Based Spatial Soundfield Reproduction Using an Irregular Loudspeaker Array

“…Since Gerzon developed velocity and sound intensity theories of sound localization for reproducing psychoacoustically optimum sound [23], acoustic quantities containing directivity information, such as particle velocity and sound intensity, have been controlled in soundfield reproduction systems to improve the performance of perceptual localization. In addition to good performance for regularly or evenly placed loudspeakers [24]- [27], the particle velocity or sound intensity based methods also perform well in irregular loudspeaker arrangements. A sound signal conversion method between different loudspeaker systems is proposed in [28], which reproduces the spatial impression of the original sound by maintaining the pressure and direction of sound (controlled by particle velocity).…”

Particle-Velocity-Based Mixed-Source Sound Field Translation for Binaural Reproduction

“…Since Gerzon first developed velocity theory of sound localization based on binarual phase cues for reproducing psychoacoustically optimum sound [41], particle velocity (vector), which is recently controlled in sound field reproduction systems [42][43][44], has been one of the objective metrics predicting sound direction. Thus, having particle velocity as the design criterion contributes to a more precise reconstruction of the interaural phase difference, which is crucial for human perception of sound directions and, therefore, contributes to improved localization of the reconstructed sound, especially for low frequencies (below 700 Hz) [45].…”