In this paper a discussion is presented of the theory for finding a set of orthogonal basis functions describing sound radiation and scattering from irregular shaped bodies. The technique is based on the use of the Singular Value Decomposition (SVD). It is shown how the 'mode shapes' of a radiating sphere, described by the complex spherical harmonics, are related to those extracted using the SVD. The method is implemented numerically, using the Boundary Element Method (BEM), for the cases of an ellipsoid, a baffled shallow cylinder (to describe the concha), and an accurate baffled pinna to show the relationships between the basis functions on the surface of the body and those in the far field. For the latter case, numerical simulations of the 'mode shapes' as investigated by E.A.G. Shaw, are also presented.
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