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Abstract
The spherical harmonic (SH) framework is a powerful representation that can be used to describe to a 3D soundfield. It decomposes waves propagating through space into a sum of infinitely many SH functions, a set of orthonormal basis functions over the sphere, and a set of source-dependent soundfield coefficients. The coefficients encode spatial information about the source and a wave propagation model. 3D soundfields can be captured or recorded using microphone arrays, manipulated or modified to enhance or reduce contributions from certain sources/locations, and reproduced using loudspeaker arrays to a degree of accuracy dependent on the array geometry. Other uses of the representation include SH beamforming, source localisation and isolation, and acoustic holography.
This thesis focuses on the processes of coefficient extraction and some aspects of soundfield manipulation. Traditional extraction methods seek to gain a representation of all sources within the soundfield to a greater or lesser degree of accuracy. This thesis attempts to extract only the contributions from certain sources, spatially filtering the soundfield. The extraction process (involving discrete spatial sampling) introduces errors into the SH representation, in particular those of truncation error (TE) from using only a finite number of coefficients to reproduce a soundfield and spatial aliasing (SA) errors in the extracted coefficients. This thesis derives several closed form solutions for the TE (excluding SA) under various soundfield conditions, and shows the connection between the plane and spherical wave cases. It also investigates the patterns of SA caused by the regularised inverse (RI) and orthonormal extraction (OE) methods and observes the combined effects of SA and TE for a particular spherical microphone array. This thesis proposes a spatial Wiener filter (SWF) that makes use of infinite spatial order prior models of the propagation model, source power and location to reduce SA errors and to reduce the contribution of unwanted sources to the coefficients. The RI and OE methods are analysed in the same manner and the SWF is shown to be superior at reducing SA. The SWF is then extended to a finite spatial order case. These methods are compared under various spatial scenarios and show the benefit of the SWF and eliminating an unwanted source, using the proposed measures of total mean square SA error and mean combined truncation and SA error.