Analysis of partially coherent acoustic wavefields from multichannel sound reproduction systems

Abstract

This work analyzes the performance of multichannel sound reproduction systems using the theory of partially coherent wavefields to model the acoustic velocity vector at the listener’s location. In this framework, the original signal is modelled as a narrowband, locally stationary random process, defined by a coherence time. The system model incorporates attenuation and delays from both positioning of the listener relative to the loudspeakers and any processing used in the reproduction system (e.g., panning). Given the finite coherence time of the signal, the magnitude and direction of the resultant velocity vector fluctuates in time. The location and spread of the virtual source that a human listener infers is determined by the distribution of velocity vector directions and a psychoacoustic averaging time associated with the precedence effect. Using this framework, we demonstrate the relative importance of three time constants in forming a stable image of the source location: the signal coherence time, the acoustic decay time, and the perceptual averaging time. This framework can be extended to incorporate early reflections in the listening environment and generalized to encompass natural sounds, such as speech or music, which can be modelled as a sum of narrowband components.