Theoretical advances of spatial sound field reproduction

Abstract

This thesis covers three theoretical advances of spatial sound field reproduction: time-domain modelling of spatial sound fields, the acoustic particle velocity vectors (AVVs) and multi-driver headphones.

The spherical harmonic (SH) decomposition of a spatial sound field is usually in the frequency domain. Time-domain SH decompositions eliminate the necessity of calculating Fourier transforms and may benefit applications with real-time requirements. Existing time-domain SH decompositions of spatial sound fields are mostly limited to point sources and plane waves. Most sources have directional characteristics, which are encapsulated by the source's directional impulse response. This thesis proposes the higher-order spherical delta function, which is a spherical wave front with direction dependent amplitude. The source's directional impulse response is then modelled as a sequence of higher-order spherical delta functions emitted at successive time instances by the source. In spatial sound field reproduction, the impulse response between the source and the listening region is often measured or modelled. This thesis proposes the time-domain modelling of the source-to-surface impulse response, which is the time-domain signal observed on a spherical surface (e.g., the boundary of the listening region) when the input to the source is a Dirac delta function. The source-to-surface impulse response is modelled as the intersections between the sequence of higher-order spherical delta functions emitted by the source and the spherical surface on which the impulse response is observed.

The AVVs are related to human's localisation of sound and can be used in spatial sound field reproduction. To characterise the AVVs in the listening region, this thesis proposes the SHV-indR and CHV-indR coefficients, which are the radially independent SH and cylindrical harmonic coefficients of the AVVs, respectively. The SHV-indR and CHV-indR coefficients allow the computation of the AVVs in the listening region via spherical or cylindrical microphone array pressure measurements, and eliminate the necessity of measuring the AVVs point-by-point. Moreover, while previous work has proposed the SH decomposition of the AVVs on a spherical surface, the radial independence of the SHV-indR and CHV-indR coefficients allows the characterisation of the AVVs throughout the entire listening region without decomposing it into multiple concentric spherical surfaces. This thesis also proposes velocity matching, which reproduces the SHV-indR or CHV-indR coefficients of the desired sound field.

Headphone-based binaural reproduction usually requires an estimate of the listener's HRTFs, which could be challenging to obtain. The human head and body can be modelled by simple geometric models, yet the shape of the pinna is highly complicated. To deliver personalised pinna localisation cues, multi-driver headphones were proposed, which utilised additional miniature speakers in the headphone enclosure to augment the side driver. The sound waves emitted from the miniature speakers interact with the pinna, and the localisation cues due to pinna reflections and scattering are naturally introduced. Instead of using miniature speakers as an augmentation, this thesis proposes using an array of MEMS speakers inside the headphone enclosure to reproduce the AVVs on a surface that covers the ear. The target AVVs account for the reflections and scattering of the incident sound field by the human head excluding the pinna, since reflections and scattering by the pinna are naturally introduced by the MEMS speakers within the headphone enclosure. Unlike previous work, which used BEM to calculate the target AVVs, this thesis proposes a geometric model for estimating these vectors using only pressure measurements from a spherical microphone array located at the listener's head location. Show more