Orthogonal radiation patterns for three-dimensional noise sources based on the spherical harmonics of sphere(s)

The control and thus sensing of radiation from three-dimensional noise sources has become a topic of strong interest as investigation moves away from the laboratory. Furthermore, the advance in signal processing power has facilitated the real-time fusion of a large number of sensor signals, which are typically required to give an accurate estimate of global error signals. Current state-of-the-art designs have typically been based upon a BEM or FEA analysis, which are as complicated as the structure under investigation. However, the exact nature of a global set of acoustic orthogonal patterns and their practical measurement from large threedimensional sources remains elusive. In this work we examine the spherical vibration modes of sphere(s) as a basis function for describing orthogonal radiation patterns with respect to radiated sound power. The spherical harmonics form an orthogonal set of vibration patterns on the surface of the sphere, which we show can be used to formulate a set of orthogonal (to sound power radiation) sound pressure patterns. The novel work contained in this paper has two aspects; a development of orthogonal radiation patterns based on more than one sphere; and a development based on spheres in both the acoustic free field and a half-space. The results have implications in the area of acoustic modelling and also in the area of sensing system design for active noise control.