Error analysis of spherical harmonic soundfield representations in terms of truncation and aliasing errors

The use of the spherical harmonic representation of a soundfield is useful when attempting to record, reproduce or manipulate the spatial qualities of the soundfield. However, the practical requirement of discrete sampling in the spatial domain brings errors to the system, namely those of truncation and spatial aliasing. The truncation error can be seen in the synthesized pressure, while spatial aliasing is apparent when looking at the spherical harmonic coefficients themselves. These errors are linked to each other through the number and position of the microphones in the array, as well as the method used to perform numerical integration on the sphere, but they can exist separately. This paper discusses the above topics and investigates two approaches to numerical integration in regards to sampling the soundfield using an em32 Eigenmike^® microphone array.